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)
For those that don’t know; https://www.youtube.com/watch?v=IehQRVylI0U
Though the version most people are familiar with is actually a cover; https://www.youtube.com/watch?v=8G_L9tXEwmc
(I am, begrudgingly, forced to admit that the Captain Tractor version is better)