The Coffee Song by Frank Sinatra - I love coffee. I love Frank Sinatra. The theory of logic makes it so I have to love this song.
Everybody Eats When They Come to My House by Cab Calloway - oh Cab, you're so great. This song is catchy, funny, and represents a time when food was harder to come by; I imagine that's what inspired songs like this.
Rock 'n' Roll McDonald's by Wesley Willis - you mean to say you didn't know about schizophrenic musician Wesley Willis, that just sings absurd and bizarre lyrics over the same keyboard music? Well, this will be a good introduction for you. In case the song sounds familiar to you, it was in the film Super Size Me.
Rubber Biscuit by the Blues Brothers - originally done by The Chips, this song is weird and makes no sense as it's mostly scat singing. The Blues Brothers version is my preference. I wish I could scat.
All That Meat and No Potatoes by Fats Waller - Fats clearly has some strong opinions about what should be on his dinner plate.
Spam Song by Monty Python
They're Red Hot by Robert Johnson
Nutrition by Dead Milkmen - If you don't give a shit about anything else, care about your own nutrition. (If you're like me and don't listen to a lot of punk and can't tell what he's saying, lyrics are here.)
Eat Steak by Reverend Horton Heat - a damn good song about steak by a damn good rockabilly band.
Satan Gave Me a Taco by Beck - a warning against taking any food, especially tacos, from Satan. From a pre-"Loser" Beck album, containing mostly his own home recordings and random noises.
And finally, don't forget about Weird Al's entire Food Album.