I think In the Navy sung by the Viking Pigs pillaging a village to be a rather weird touch on that song. The big joke being that the Navy was once an old term used to refer to the Vikings.
And then there's all those whatnot skiers singing Tumbling Tumbleweeds as they crash into trees or each other some of them literally tumbling cartwheels just like tumbleweeds.
Then there's When the Saints go Marching in performed by Hal Lynden and the Electric Mayhem while silly old Beauregard is testing trapdoor releases for the stage and they fall down but climb back up and resume singing.
Finally my favourite muppet show skit is really pretty weird when you come to think about it. The Happy Wanderer sung by three pig alps-climbers who fall off one by one. A very weird bizarre dark twist on what is supposed to be such a jolly happy sort of song.