Came here for this, but you simply MUST include ‘Storm’. It’s great, and I think it’ll play well here.
Thank you for those links. He is hilariously funny and I never would have heard of him otherwise. 
Bill Burr
I saw him recently at the Count Basie Theater in Red Bank, NJ and it was the best comedy act I’ve ever seen. His new stuff was even better than in the above links.
His stand-up is great too: http://www.youtube.com/watch?v=r0HNu77t354
And he can deliver serious and emotional songs: http://www.youtube.com/watch?v=exwn6fuF9y0
He’s currently touring the US and has a couple of dates in Canada: http://timminchin.com
Jim Gaffigan:
Damn you for stealing my comedian! You even chose two of the clips I was going to use!
Well, we’re allowed three, so I have to get a third…I’m tempted to do his bit on ketchup, but then everyone will think he only does fod jokes, when that’s not true (it’s only like 80% food :p) so I’ll go with holiday traditions:
That’s awesome.
While we’re on the subject of Tim Minchin, I’ll add my favorite clips (in addition to the aforementioned “Storm”).
Tony the Fish - > Take My Wife - bit on evolution and a song about general skepticism.
As was also mentioned, he can deliver powerful emotional songs along with his humor, and I can think of no better example than his brilliant Christmas song White Wine in the Sun.