Weird al is a rather obvious.
But Axis of awesome is also a sheer favourite of mine. their four chords song is a genius composition mashup of many iconic songs throughout the years.
Whitney Avalon is a very underrated one who does some really good and rather witty pop culture themed songs.
Least favourite: Dennis Leary (He lives up to his name)
Would the Bloodhound Gang be considered comedy? always loved Bloodhound Gang. sure they had that one song but the CKY videos introduced me to their other stuff which is quite good.