These are Konoko's moves.  Click on the name of a move to open a picture of the move..
Triple-Hit Haymaker
I assume you know how to punch and kick.  If you don't, go read the manual or play the game. tutorial.
Difficulty: 1
This move is incredibly easy to pull off. It's 3 punches in a row.  It will knock down your opponent.
Spinning Sidekick
Difficulty: 2
Kick, kick, kick.  It is quite easy.  However, it takes much longer to do than the 3-hit haymaker.  Sometimes an enemy will smack you while you are trying to get this move.
Willow Kick
Difficulty: 1
Press Back, then Forward and Kick.
This will kick your enemy in the groin.  The enemy will double over, allowing you to (my favorite) do a Sledgehammer Heel upon him.
Sledgehammer Heel
Difficulty: 3
Punch, punch, kick
This move is invaluable.  You will find yourself using it even in the last level.  The main use of this move is to kick people on the floor.  Attempting this move while your enemy is standing is quite hard, however, if you can hit them with the kick, your enemy flies a long way.
Crescent Moon Kick
Difficulty: 3
Kick, kick, then forward + kick
Konoko's Diary suggests this move shold be used against jumping opponents, but the move takes too long to set up.  Instead, I use it if I'm bored of normal moves.  It looks dandy too.
Running Lariat
Difficulty: 2
While running, press Punch
Ouch! That's what you should first say when you do this move.  Konoko grabs an enemy's head, jumps, and spins... CRACK!  You also get to kick whoever's standing behind the poor snapped guy.
Rising Fury
Difficulty: 4
Crouch. Then let off crouch and press Punch.
I find this move very useful.  You can hit people lying on the ground with this move.  Also, you can move in midair while performing the move -- so you can hit one person going up, move a bit to the right, and smack another going down.
Devil Spin Kick
Difficulty: 4
Crouch. Then let off crouch and Kick.
Quite possibly the most useful move in Oni!  Konoko does 3 spins with her foot extended... connecting with any chins that happen to be in the way.
Twister Kick
Difficulty: 5
Move left, then press forward + kick.
This moves looks cool and is a bit useful.  The worst part about it is that it's very tricky! You can't let Konoko actually move left.  Instead, just press left quickly and then do the keys of the Willow Kick.  It may take some time.
Front Pistol Disarm
Difficulty: 2
Standing in front of enemy, forward + punch
Easy. Your enemy must be holding a pistol for this to work.
Back Pistol Disarm
Difficulty: 3
Standing in back of enemy, forward + punch
Cool arm-creaking move.  The main trouble is getting in back of the enemy in the first place.
Front Punch Throw
Difficulty: 3
In front of enemy, forward + punch
This isn't a great move. It doesn't do too much damage, and throws your enemy too high to hit any other people around.  Also hard to do as it usually becomes a backhand.
Front Kick Throw
Difficulty: 2
In front of enemy, forward + kick
Great move. It's very easy to do, throws the enemy back quite a ways, and hits other enemies in the flight path.