The humor in Avatar is very light-hearted and not trying to be anything more than that. When it does happen it's not side-splittingly hilarious but it's still effective without needing to go to any extremes, the writers could almost be called geniuses for finding that perfect balance.
Most of the love for Sokka stems from the fact that he's an extremely well-rounded character going through a pretty deep arc (or even multiple arcs), him being the comic relief is just one of his more memorable aspects. He can be serious, protective, sarcastic, intelligent, stupid (
really stupid), sexist, loving, determined, close-minded, adventurous, etc all at the same time while
still maintaining a personality and not coming off as completely schizophrenic. Only one word can describe him: "Adaptable".
I'm just going to link you to his Personality section of the wikia:
http://avatar.wikia.com/wiki/Sokka#Personality
Also if you didn't genuinely laugh at Sokka's role in The Desert then I'm afraid your humor standards are simply too sophisticated, and you need to lay back and drink some cactus juice :S
It'll quench ya'