The ironic part is that the Simpsons was pretty much centered on a stereotype of the American family, with Homer being a really unflattering caricature of the average working class male.

Apu, in comparison, seems like a pretty flattering depiction of a south asian. Compared to Homer, he is kind, clever, and successful.

Most stereotypes are false in that most real people (ones that aren't trying to fit a stereotype) don't fit perfectly into any stereotype.

A stereotype is an averaging of attributes. Humor based on stereotype is funny often because it is accurate to a point where people have to grudingly agree with it.