Any one of many by Jake Thakray of the British Isles! I belive that his very funniest of all might be "Sister Josephine". 2 others that come to mind: "When Ulysses Comes Home" and "On Again, On Again, On"
Eric Bogle's "He's Nobody's Moggie Now" and his "Plastic Paddy". As for the one he wrote about not being "willin' to sing Bob Dylan", I heckled some folk club president unmercifully while he was singing that one, and then got up on stage after him and made SURE to sing a couple of Dylan songs, just for him. He was a pretentious git, anyway, making fun of Mr. Bob like that. Bob's version of "Barbara Allen" would make his version sound like a piece of soggy milquetoast. :-)
A number of Dylan's songs from the 60's have some very biting humour and irony in them, although they are not strictly funny songs as much as they are a form of social satirical comment...and "exercises in tonal breath control", of course.