Funniest kill that I did?
It was either the series of kills that I got on Vi (she'd come to lane, I (Jax) would just jump on her, stun her, and kill her. Rinse and repeat for the entire lane phase.
The other option was when we had just got done with a teamfight (we won barely), and a Rengar jumped me as Amumu and a Nunu when we were being in a brush. Nunu dies, so I flash out, stop, say "screw it," then bandage toss back in and kill him with a quick tantrum.
Funniest assist was right at the beginning of a match. I was Nunu Support with a Draven. We have to leash blue, so we are late to lane, but I Blood Boil him, and he runs through the bush, just hammers both the sona and ashe, giving him a double kill. It was honestly pretty funny because he literally ignores cs and everything just to be a murderhobo.