There's a whole world of insults out there! From disparaging your opponent's parentage, denigrating their intelligence, making fun of clothing, and saying your opponent is ugly or cowardly--all these are acceptable.
The insults you put forth are fairly tame. If you are worried about violence in them, you must not be writing for an American audience. Successful YA novels are rife with violence. Sex not so much. YA is written for teens. And teens have been exposed to much worse than "go sit on a rusty nail." "Hang yourself" is fairly blunt really. That's not really an insult, that's a suggestion to kill yourself. It really depends on what you want your insults to achieve. "Eat sh*t and die" was a popular one when I was growing up, punctuated by rude gesture, generally as a conversation ender. But prior to that there was a build...
"eat your deads?" I have never heard that one and have no idea what it means...
You can certainly get more creative.
"Maybe if you ate some of that makeup you'd be pretty on the inside." (found that one on the internet).
It also depends on if this is here on earth, or in a created reality (like the Hunger Games). You can create subs for cursing in a created reality. Gorram it! Watch your fracking language!
Also, look to Shakespeare, that guy was pretty darn good at it. It's not hard to go through this list and update it.