Most of the Basement Tapes songs have some funny turns of phrase ("the comic book and me, just us, we caught the bus."), but two of the unreleased songs from those sessions that circulate among fans are downright hilarious: a doo-wop parody called "I'm Your Teenage Prayer" and bit where Dylan and The Banddeliberately slaughter a Mexican ballad.
On The Bootleg Series VI: Live 1964, recorded just as Dylan was trying to break free of the Protest Singer mold, he is very clearly baked to the gills and in a very good mood. For instance, his reaction to an audience member requesting "Mary Had A Little Lamb".
The travails of the narrator of "Just Like Tom Thumb's Blues" get rather amusing, even if you feel sorry for the poor sap. His Screw This, I'm Outta Here! reaction to end the song caps off the tour de force.
"Foot of Pride", for all its Crapsack World-ness, is hysterically funny.
He looked straight into the sun and said "Revenge is mine!" ...But he drinks, and drinks can be fixed.