I think that Editor 1's ideas are the best thing to start with. They are, however, a little naive if the bully in question is truly a sociopath. Some bullies will look for paybacks if you out them, especially if it's to officials that want to just smooth things over and avoid the problem. If you do this, make DAMNED SURE that you follow through with the multiple, documented, multi-tier approach. That gives you the best chance to actually get some action on the problem.
I was bullied through most of my school years. In my junior year of high school, I started learning how to stick-fight in armor. As soon as that became known, the bullying stopped. It was not necessary for me to actually beat anybody like a harp seal; all that was needed was for them to know that I could. Do not take the advice to actually beat him with a club. That is far more legal trouble than you could possibly want. Do not confuse the All-American revenge fantasy with the truth. That being said...
When I was in my twenties, I had a roommate that had problems with an adult bully in our neighborhood. My roommate had a junk car. Before we called up the wrecker to tow it, we took turns shredding on it with medieval edged weapons. Word got around. The bully stopped even making eye contact with my roommate. When we moved to a different house, we did the same thing with a junk refrigerator. Months later, word got back to us that the local street gang feared us. I'll admit, street gangs back in my youth weren't half as serious as they are nowadays, but still... Let weirdness and tacit threats work in your favor. Bullies fear what they don't understand, or haven't experienced. Public displays that you maybe might be a dangerous monkey will grow in the telling. You shouldn't have to directly threaten anybody. Let their fearful imagination work on them.
Now, as to the verbal harassment, I understand that the stuttering would make the usual give and take really one-sided, so don't go verbal. Go written. Find some written outlet where word could get around. Study satire, humorous metaphor, dramatic irony; learn how to use words. See if poetry works for you, or rap. The journalist Hunter S. Thompson avoided a few complications with police simply by telling them who he was. That's because nobody wants someone with a sharp wit to pillory them in public. Nobody. As the slam poet Larry Francis once put it: DON'T MAKE ME WRITE A POEM ABOUT YOU!
Good luck to you. Again, start with Editor 1's suggestions. Just try to make sure you have a backup plan or three. Eschew revenge, and remember that your opponent is, in the final analysis, a pathetic creature. Defeat him and his allies as gently as you can. Either he will change his ways, or life will beat him to death, slowly. A few years ago I saw one of the demons of my youth, and he was then a fat wino, belly distended high from a hardening liver. It struck me then, how one hard punch to the belly would probably send him straight into hepatic failure, but he was failing just fine without me. All the demons of my youth had their own demons, and they have been eaten up. Concentrate on improving your own life, instead. Get past this and move on as quickly as you can, and don't look back. The best revenge really IS living well.
