Am I the only one who thinks it's a bit odd that Ulfric's body and that of Galmar don't disappear after they're killed? Is it a bug or an intentional macabre part of the game?

It's got to be a bug, because Ulfric still has his head. Tulius intended to take it for a trophy. So if he left the body to rot, it would be headless. And it certainly wouldn't be stinking up the new jarl's palace.

I kind of want to imagine it as so.

Got to be a bug. Tullius was meant to ship his head to Cyrodiil or something. Not sure if that was a joke from Tullius, but it seems ridiculous that you would leave the rotting corpses of a dead Jarl and his man servant on the floor of your palace.

That's what I thought, unless it was a way of warning others who might have similar ideas. But if so they wouldn't leave him just lying around a royal palace! They'd have him strung up on the city main gates or something.

Definitely a bug. Who would want a rotting corpse in their main hall?

I dragged the bodies into the map room. I knew I wouldn't have any errands there anyway, so now I can just pretend that their heads in fact got sent to Imperial City and the rest of the bodies got burned or buried or whatever.

You could Dead Thrall them and then dump them into the Temple of Talos.

Unless your level is too high... I think Galmars cap level is 40 or lower, but Ulfric might be too strong for you. Also keep in mind that his level is higher than your own.