Joe Hall's great Canadian classic Vampire Beavers is in a class by itself (especially when it breaks into The Maple Leaf Forever parody). Two of the funniest songs of all time are by Spike Jones. His version of "Laura" has ruined that ruinable song for many, many people. Even funnier is the Dog Love Song.
Paul Anka's song, "She's Having My Baby" is the funniest song I know, but for all the right reasons.
yours, Peter T.