No, you are certainly not over reacting.
I have 2 boys aged 10 and 8, and those words/ that behaviour is not even a little acceptable. Same as Alpha; yes, they get a little goofy, and yes, farts and burps are funny. But if they get too crazy, it's nipped in the bud. Sexual jokes of that sort are definitely not heard around here.
He's absolutely getting it from home, it's obviously okay there.
I would sit at the table with the two of them and figure this out. Explain in a very no-nonsense voice that you do not like the way they have been behaving. Get a piece of poster paper and make up a list. "We are expected to.... (use indoor voices, not shout; use walking feet, not run; use proper language, etc)". Post it up for them in a common area. When they get rowdy, point to the poster and remind them ONCE. After that, they get separated. If that means they both sit in a chair for the rest of the afternoon in different corners of the room, so be it! Make sure that they know exactly what will be happening. And (I say this hoping you don't get offended); please give them both the same consequences. I know that this boy's influence is what is causing his behaviour, but this is a great time to learn that just because the people around us are doing something, doesn't mean we have to.
Lastly- have you discussed this with mom and dad? What are their reactions/thoughts? If they are laughing it up at how "funny" he is, I would be having a serious chat. If they don't smarten up (and smarten him up), then he would totally be "outgrowing" my program at the end of the school year. Can you imagine doing an entire summer????

Some friends of mine have a BOYS WILL BE BOYS attitude. And it has turned their kids into BOYS WILL BE TOTAL JERKS. My two cents.... or did we decide it's a nickel now?