Well, to make it funny you need a bounty in Whiterun.
Spoiler
When Odahviing is first fought, there's a guard who's scripted to die. Walk up to him, call Odahviing, and then initiate conversation, which will have you being in the middle of being arrested.
I... don't really remember. I'm guessing it would be something to do with Cicero and the Dark Brotherhood. Nothing else seemed like it was trying to be funny. Although watching a farmer try to sacrifice a cow, only to get hammered into space, is usually good for a laugh or two.
I opened up the race menu before the carriage arrived at the execution site and the result was the thing doing barrel rolls, going infront of the horse, and every combination one could think of.