Mortal Kombat/Street Fighter Attacks

3d studio max with it's postproduction features would handle the stuff you're talking about, but it's pretty expensive, student version cost about $1000 or so.

blender is a free animation program, i've only played with it a little so i cant recommend it, although i do think it has serious potential. there are links to it further down te page.

of course the standards like after effects, photoshop, premiere will be able to do some of the stuff you want to do.

basically i think you'll need a few programs to do it all.