There are some interesting differences between these four words.
The word, STOP, primarily means to bring to a halt or end movement.
You could say, I stopped him from eating the rest of the ice cream by knocking it out of his hand.
You physically stopped him!
The word, QUIT, means to give up or cease.
You could say, I want to give up eating ice cream. I will quit!
I will never eat it again.
The word, PREVENT, means to take action in advance.
You could say, I wrote a list of things to buy at the grocery store. It did not include ice cream. Having this list prevented me from buying ice cream.
The word, AVOID, primarily means staying away or at a distance.
You could say, I avoid opening the freezer door. If I don't see the container, I don't think about eating ice cream. I do what I can to avoid ice cream.
I hope this helps.