For the animations, one thing you should really focus on is punchiness. You're almost there with the speed of the actual attacks (i.e. the gap between the windup and strike), but they still feel kind of slow and muddy.
As a general principle, the animations should have a smooth gradient from anticipation -> attack -> follow through.
Come to think of it, all of them but the knife attack are missing the follow through entirely. It makes a huge difference in showing momentum, a punch that take a couple frames to come to a stop feels way more powerful than one that stops immediately on impact.
Something as simple as deleting a couple frames to speed them up and adding some follow through would probably really improve them.
Also, when you're animating things like these, most of time less is more. Look at this for example-

The slashes are just one frame each, so the sword jumps from being all the way back to all the way out, but the arc implies that it moved super quickly that entire way, and the combination of the arc fading and the arm slowing down gives that movement a little accent that makes it more fluid and believable.
Think about pixel art in general- you use a small amount of resources to give the impression of something greater than you're actually making. So instead of padding the animations to make them smoother, try making it feel as good as possible with as few frames as possible before you worry about how it looks. In fact it would probably be better to just sketch it out with a stick figure until the movement is right. Like wolf brought up consider dramatic poses.