Haven't read every message but didn't see these anywhere:
"Alice's Restaurant" by Arlo Guthrie -- more of a one song set in an act than a true song but it's funny as hell, especially if you "came of age" in the draft era (1970 plus or minus about 5 years) and had to take a draft physical. "The Motorcycle Song" was pretty good too.
Someone mentioned Ray Stevens and, yes, he had several albums worth of comical songs. I think my favorites may have been "Ahab the Arab" (very early in his career), "Along Came Jones" and "The Shriners' Convention."
On the Celtic music side, one of the best might be "Seven Drunken Nights." The version I have is by the Brobdingnagian Bards but I think it's been done by a lot of groups. The basic song is funny but the way it's performed adds a lot too, especially the way the Bards do it.