I can't help it - it implies that you have a choice outwardly, but emotionally you can't do it. "I can't help it - I just don't like peas." There is nothing in the outside world that would make you dislike peas. It is just a feeling you have that you can't overcome. I can't avoid it. - You don't have a choice. Some outside force is making do or not do something. Your feelings are not involved. "I can't avoid it. I have to go visit the doctor about this knee." "It looks like I can't avoid having to take French this semester. I need it to graduate."

"I can't help it" is an expression that means something like "I can't stop myself from doing something." It's an excuse for having weak willpower or not taking responsibility for what one does. Example: "She can't help it. She can't stop herself from petting every cute little dog that she sees."