Overly sensitive? I think they are scarcely sensitive.
Trying to communicate how it makes you feel would be a sage advise, but if you are considered a clown, nothing coming from a clown is to be considered serious.
You have to take steps. It depends on yur age, but you have to assert your position in the only possible way, by withdrawing. You won't go to eat with them and you will not stay in the middle being ridiculed. Just stand up and leave. Your mom says you are too sensitive? Yes, you are, and that is why you can't affrod staying there. They're just kidding? Yes, and you don't like it. One may NOT accept jokes, right? So you don't have right to forbid jokes, but you have a right to get away.
An italian proverb says "meglio soli che male accompagnati" which means it's better to be alone than in bad company. It is your case.

The best of luck!