Elise is an incredible top who's very complex and hard to play. Ap, Ad, Bruiser or hybrid - she's powerful. As AD she's one of the stronger tower killers(think Yi level of tower killing). She has no real escape, but she can delay the inevitable, which will occasionally save you. She has a skill shot stun, and can follow it up somewhat well. As a jungle, she has one of the strongest ganks in the game due to her 950 engagement range, she can engage anywhere in lane from the bush. Crazy ganks, scary top, and snowballs fairly hard. She's not an assassin, needs to be played Methodically.
Kha'zix is the king of snowball, one of the fastest wave clearers in the game, along with(post-6) one of the strongest long range pokes - Evolve his w and destroy everything. Great escape mechanics, Decent assassin...He does lack the burst though - his damage is very high, very sustained, but he is very squishy, and easy to shut down. Good champion, but you will be punished for mistakes HARD.
Fizz is an amazing mid, that takes an entirely different mindset from other mids to play. He can dodge almost any major ability with his troll-pole(Playful Trickster), on a low 18 second CD(roughly). Has some of the most ridiculous AP scalings, he does insane damage, can move very far, and can be played relatively(relative to the others in this list) easily. Solid mid, questionable jungle. One of the highest damage mids in the game, should be in every mids roster.
Zed is an interesting champion that I just haven't quite gotten the hang of, so I'll let someone else comment on him.
Elise is good in almost all scenarios, she can be built for any team. Fizz is an AP mid only. He's generally bad on top, countered by most tops. Kha'zix is great top, meh in the jungle pre-6. Great ganks in jungle, easily shut down if you play poorly, though. I don't like Zed.