Everybody Was Kung-Fu Fighting

If you haven't seen Spwack's Finders Keepers, go have a look. The character generator is absolutely glorious.

Demon Flips the Cart style
From Kill Six Billion Demons.

 
Anyway, I've recently seen such wonderful films as the Invincible Armour or the Five Deadly Venoms, and they got me thinking that Finders Keepers lacks some nice, dirt simple martial arts. Thus the list below. As it was envisioned for an Into the Odd adjacent rule set, it assumes hp as stamina - very low and easy to recover after a fight, plus you only start taking real injuries once you are at 0 hp. But it wouldn't be an OSR if you couldn't tweak the table to fit into your own wuxia game.
 

From Exalted.

    
Instead of a weapon, you can start proficient in a martial arts style. You can use one style at a time and it takes an action to switch between styles you know. No weapon-based martial art styles were included, so you can only use martial arts while unarmed and unarmoured. If one of your party members knows a different style than you, you can train with them and gain that style once you level up / spend enough XP.

Each martial art comes with a trick, many of which do something with no save / no roll, or grant some immunity. When two martial artists fight, a perfect defense always beats a perfect offense. Thus if a Jiu-Jitsu user tried to knock prone a master of the Jade Mountain Stance, they would fail. Otherwise, you can use the tricks at will.

Optional Rule: Odd Stunts
If you describe your attack in a cool way that incorporates your surroundings (kicking a table at your foe, running up a wall for a backflip kick), the GM may enhance your damage roll.
 

Elemental Bending: Fire style
From here.

 

d60	Style Name	Dmg	Trick
1	Aikido	d6	When you successfully dodge an attack, you redirect it back at the attacker.
2	Capoeira	d6	When reduced to 0 hp, immediately gain an extra turn. You may drop to 0 hp at will.
3	Celestial Monkey King style	d8	Once per enemy, you may disarm, trip or pickpocket them with no save.
4	Charcoal March of Spiders style	d8	When you roll max damage, you may remove one of your foe's magical or combat abilities until they rest.
5	Demon Flips the Cart style	d8	You can automatically succeed on a STR check by dropping to 0 hp.
6	Dreaming Pearl Courtesan style	d6	Step up damage if you're prim and proper, and again if your foe could be sexually attracted to you.
7	Elemental Bending: Air style	d6	You can push air to project your strikes at range. You can double jump.
8	Elemental Bending: Fire style	d6	Your strikes can deal fire damage. You take half damage from fire and heat.
9	Elemental Bending: Metal style	d10	Metal weapons shatter when they strike you. Still take the damage normally.
10	Elemental Bending: Water style	d8	Breathe and move freely underwater.
11	Elemental Bending: Wood style	d8	Plants never harm, snare or slow you down. You can climb trees and move between treetops at full running speed.
12	Falling Cherry Blossom style	d6	You fall as a feather and can jump or glide long distances.
13	Fierce Horse Soul style	d8	You run as fast as a horse and can run forever without tiring.
14	Five Deadly Venoms: C	d8	You may decide to impair your damage, but attack everyone in reach.
15	Five Deadly Venoms: Lizard style	d6	You can run on walls and ceiling until you stop moving.
16	Five Deadly Venoms: Scorpion style	d8	Your strikes can deal either bludgeoning or piercing damage. Roll damage with advantage against unsuspecting foes.
17	Five Deadly Venoms: Snake style	d8	Your strikes are fast nobody can even see you move. No counters, dodging or defensive actions are possible.
18	Five Deadly Venoms: Toad style	d6	Take 1 less damage from all sources.
19	Five Dragons As One style	d6	For each ally in the fight that also knows this style, gain +1 damage, to a maximum of +4.
20	Head of John style	d6	Your head is completely invulnerable, both to physical and mental effects.
21	Hungry Ghost style	d6	Ignore all special defenses (like intangibility or invulnerability).
22	Jade Mountain Stance style	d6	You cannot be moved, tripped, etc. Gain a free attack against anyone who would try.
23	Jiu-Jitsu	d6	You can knock prone anyone, no save, as long as you also fall with them. You deal full damage in a grapple.
24	Judo	d6	When you roll higher than your foe, you may decide to deal no damage and instead reposition them with no save.
25	Karate	d8	If you have enough time to properly concentrate, you can punch through any inanimate obstacle short of adamant.
26	Ki Rata	d12	Whenever you roll 10+ on a damage die, add another die. If you roll 3+ dice in a single attack, all the bones in your arm shatter from the strain.
27	Kickbox	d8	While at full hp, reroll all 1s.
28	Krav Maga	d10	When you roll higher than your foe, you may decide to deal no damage and instead disarm a weapon-wielding attacker.
29	Krayu Mat	d8	You can spend a round focusing your ki to fire a beam of pure energy on your next turn, dealing your unarmed damage to everyone in a line.
30	Kung-Fu: Crane style	d8	Your attacks have reach as a spear. You never need to roll for balance.
31	Kung-Fu: Dragon style	d10	Murder one low-level mook per round, no questions asked. Must be indistinguishable from all other mooks.
32	Kung-Fu: Mantis style	d8	When you roll max damage, you may maim your opponent.
33	Kung-Fu: Panda style	d8	Advantage on STR saves with your hands pressed together.
34	Kung-Fu: Tiger style	d8	Your strikes can deal either bludgeoning or slashing damage. Roll damage with advantage when you can run and pounce at your foe.
35	Laughing Wounds style	d10	If you die in combat, you may continue fighting for 5 more rounds while laughing madly.
36	Leisure Kicks style	d6	When you roll max damage, you may reroll the damage and send the target flying.
37	MMA	d8	Once ever, when you fight another martial artist, you may decide that you know the trick of their style.
38	Muay Thai	d10	Make a free attack when an enemy retreats or moves past you.
39	Ninjutsu	d6	You can climb nearly anything without a roll. Only impossible climbs require (and always allow) a roll.
40	Old-school Fisticuffs	d8	When you drop a foe to 0 hp, make an extra attack.
41	Pankration	d8	Take no penalties from tight squeezes, being prone, grappled, engulfed, or tied up.
42	Pattram Sword Hand style	d10	When you deal max damage, cut off a limb of the victim's choice. This style is considered evil and its adherents often persecuted.
43	Peasant's Path	d6	You can teach this style to anyone within a week at no XP cost.
44	Porcelain Fist style	d8	You may deal max damage by taking half that yourself.
45	Pressure Point style	d8	When you reduce a foe to 0 hp, they are completely paralysed until they can regain hp.
46	Prismatic Arrangement of Creation style	d6	Choose one damage type other than bludgeoning. While at full hp, you are completely immune to it.
47	Senjutsu	d8	You are never surprised and always act first in an encounter. You can sense nearby danger.
48	Soul Reaper style	d6	Once you strike a foe, you can freely teleport behind their back as a move until the end of the encounter.
49	Straw Stops Sleet style	d6	Immune to ranged attacks if aware of them. Your choice of dodging, deflecting or catching them.
50	Taekwondo	d6	When you attack, deal the higher of your damage roll and your opponent's roll.
51	Tai Chi	d6	You can walk on top of snow, or twigs and leaves. You can run water surface. You leave no footprints.
52	Tenfold Ebon Shadow style	d6	The first attack you ever make against each individual enemy deals 1d20 damage, but only if you know their name.
53	Void Lotus style	d6	Specify a duration to lock yourself out of time, becoming inviolable. If you have an immovable rod, you also become locked in place.
54	Vulcan Nerve Pinch style	d6	You can forgo doing damage to instead stun the enemy for half the rolled number of rounds.
55	Way of the Masters	d8	You can teach this style to any animal, and talk with any animal that knows this style.
56	White Hand style	d6	Your hand counts as a shield. "Sundering" doesn't destroy your hand, but you will have to meditate to recover.
57	Wrestling	d6	A flashy finisher can instakill anyone at 0 hp with no save and force their allies to roll Morale.
58	Zui Quan	d6	When drunk, you automatically counter-attack against all enemies that strike at you.
59	25 Purities Path	d6	As long as you lead an ascetic life, you are immune to poisons, diseases and ageing. You also need only half rations.
60	49 Empty Palms style	d8	Your attacks count as blessed if you ask for forgiveness before attacking.

From Doctor Strange.

 

As a side note, this is quite useful.

Ancient Artifacts of Stupendous Science

There are interesting gadgets that your players can find when prowling the wasteland, and then there are these things. They were rare and expensive before the Turn, and now they are the most prized possessions of the most powerful water barons, the sacred relics of hidden arcologies, or long lost in forgotten vaults.

Some might be a treasure in the big bad's lair, some a treasure the big bad seeks. Some will be the crux of their evil master plan.

All can surely be used for many a shenanigan.
  

A cruciform.
I've stolen this one wholesale from the Hyperion Cantos.
If you haven't read it, I highly recommend that you do.

 

d20 Artifacts

1. Bioprinter: From a single droplet of blood, this device can recreate and clone any creature. An adjustable fast-time field will even age the subject appropriately.
2. Recoiler: A piece of jewellery (normally a ring, bracelet or a brooch) that can be activated to instantly return the wearer to the safety of a pre-defined receiver chamber. Its range is long enough to bring one from Earth to the Moon.
3. Transmat cannon: During the Turn, these weapons were used to instantly teleport an armed antimatter bomb onboard an enemy vessel. It has a range of about a light second, a projectile chamber large enough to fit several people inside, and cannot be blocked by anything short of very advanced force shields.
4. Hypnolearning bay: A comfortable coffin where one can lie down to sleep and learn a new skill overnight*.
5. Phylacterion: A throne of chrome and wiring. When a creature is strapped into it, the phylacterion can either scan their brain and create a new mindstate disc, or download a mindstate disc into the creature's brain, overwriting their whole psyche with another person.
6. Cruciform: A cybernetic symbiont that bonds with the user and makes them nigh immortal. No matter how grisly their injuries or how little remains from their dead and destroyed body, the symbiont will eventually reconstitute them to full (physical) health. It's impossible to deactivate or detach, so users tend to be dealt with by chucking them into a volcano.
7. Becoming nook: Lie down into this surgery station and close your eyes as it anaesthetises you. One quick implantation later, you will be on your way to bionic ascension. No surgery roll is required and the recipient gains +4 bonus to their post-surgery Con Save if the becoming nook is used to add a new augmentation.
8. Warp star: A miniature black hole trapped in an indestructible crystal. Serves as an infinite power cell, capable of powering a whole city alone.
9. Gravity cannon: An unassuming platform that can nonetheless accelerate anything up to the size of a spaceship to a good fraction of c.
10. Phase gate: A cannon-like device that will charge up with 5D energy, then blast a hole to the next dimension over.
11. Nulltime tank: Inside, the time itself stands still. The grieving might keep their loved ones alive, for a certain measure of "life", while the decadent will always have their meals fresh and warm.
12. Replicator: A cloud of nanites in a box will break down matter on atomic level, then rebuild it into whatever their owner desires. While pretty much anything can be quickly fabricated, one still needs the materials and blueprints.
13. Matrix: There are many people with access to the Matrix, but this is the Matrix. Destroy this core, and the Matrix is gone. Or reprogram it to change literally anything inside. You can be a virtual god.
14. Humongous mecha activation codes: The chrome colossi of yore have lain dormant since time immemorial, but this could bring them back to life.
15. Sensory deprivation tank: The resting place for powerful psions. See here.
16. Regeneration tank: A sarcophagus-like medical device that can heal any injury, and even bring back the recently dead. Minor injuries disappear within ten minutes, a lost limb would regrow in an hour, while a resurrection might take half a day. When used to bring back the dead, however, they must Save with a penalty equal to the number of hours since their demise, or gain an insanity. Corpses that already started to rot cannot be brought back at all.
17. Time machine: When you climb inside, you can travel anywhere along the machine's own timeline, from the first moment it was activated to a split second before it will be rendered inoperable.
18. Docility drug formula: Dulls emotions, squashes all defiant thoughts. Easily spread through water supply. With a passable chemical lab, it wouldn't be hard to mass-produce the drug.
19. Small spaceship: One planet is not enough.
20. Stargate: Actually, you don't need a spaceship.

 

A phase gate, from Stranger Things.

*) Still subject to the limits on Memory.

The Old Axe

A broad, jagged axehead of black iron, its haft stained with blood.

It is said to be possessed by the spirit of a mighty warlord who stood unconquered even in death. He succumbed to his wounds yet remained standing, and the enemy forces, unaware of his demise, were so shaken by his unflinching, horrible stare that they sounded a retreat while they already had victory within their grasp.
  

  

Fearless Axe
This axe bears the blessing of courage and valour. It grants immunity to fear and advantage on Trauma rolls. Once you win a number of battles equal to twice your level while wielding the axe, it transforms into the Fearsome Axe.

Should you ever retreat from battle or otherwise prove a coward, though, it transforms into the Fearful Axe.

Fearsome Axe
This axe bears the blessing of blood and glory. It has all the benefits (and drawbacks) of the Fearless Axe, plus whenever a fear effect* successfully affects your enemies**, you channel their fear and can either heal d4 hp, or deal d4 damage to any creature in sight, no Save.

Fearful Axe
This axe bears a curse of disgrace and cowardice. You automatically suffer from any fear effect that happened near you, even if you weren't the target***, and take d4 Stress. You will never voluntarily ditch the axe, though, and always wield it in combat, even if the situation would call for eg. ranged weapons. If anyone tries to take the axe from you by force, you immediately Crack.

However, if you manage to land a killing blow regardless, the axe will transform into the Fearless Axe.
  

 

*) Including when they fail a Morale roll.
**) Only once per effect, so affecting an individual is the same as affecting a whole group.
***) The wizard casts cause fear on some orcs, the fighter tries to intimidate the lonely kobold, the child shouts "Boo", etc.