Hiii, folks! Huge "Weird Al" and Harry Potter fan here! This is post numero uno for me- huzzah!
I think that he has a little of everything, but let's break it down: he's not enough of a leader to be a Gryffindor, too nice be in Slytherin, and too social and goofy to be in Ravenclaw. The obvious correct answer, to me at least is Hufflepuff (although it is my house, too- so I may be biased)! :-)
Think about what the Sorting Hat says: 'Puffs are "just and loyal, and unafraid of toil". This is Al to a "T"! He is a really nice guy who is devoted to his band, his wife, and his kids, and was to his beloved late mommy and daddy. He works HARD and never turns down or disappoints his fans. And, he surprises people with how clever, how good-looking, and how much of a good singer he can be. He worked HARD to master the accordion, and is interested in many things without exactly being a master of them (i.e. acting, playing piano and guitar, writing, etc.) He is also REALLY nice, and a champion of all, regardless of race, gender, orientation, color, creed, etc., and extremely open-minded and flexible. He also LOVES food and has boundless energy! And, of course, he is a goofy, random science geek who is hilarious and an underdog- put him in the Rock 'n' Roll Hall of Fame or give him a Super Bowl Halftime Show, or at least host SNL, darn it! These are all very obvious marks of a Hufflepuff. Personally, I don't exactly see why our house of Hufflepuff is so hard to "read" to others, I thought were were "uncomplicated" and easy to spot right away. But I see that Al is definitely much more complicated than the average Badger.
Of course, if you beg to differ, go right ahead!!!! All opinions matter here! Us Hufflepuffs won't mind- we will tolerate the heck out of you!