I second Gaffigan and especially Brian Regan
Also, check out Uno or Pompous Clown by Jimmy Pardo
Bill Cosby-Wonderfulness was great to listen to when I was a kid, especially Chicken Heart, not sure how funny I would find it now
Kevin Bloody Wilson is worth a listen if you think you'd be interested in Australian comedic songs
For off-color songs try something by Dr. Dirty, John Valby