The only thing I dislike more than a troll is their victim. My rule of thumb is if the avatar bothering you is only a few days old and/or dressed in a way that implies they don't care about their appearance, you don't have the upper hand. Merely participating in a conversation with a troll is a no-win sitch... at best you will be in a rez area and have some tricky items that will knock around the troll and even make them crash (in which case you have just as much likelihood of getting your 1098 day old avatar suspended as the 0 day old troll).
Luckily for you, I have some super secret tactics that will help you deal with trolls and MAKE THEM PAY.
1. Typically your troll alert should go off when you see a noobish looking avatar typing out random obscenities, spamming gestures and/or holding objects that someone with a 0 day old avatar would probably not have. Immediately you should begin to assume that the person behind the computer is between the ages of 10 and 14 (as this is ALWAYS the case), and you will want to make your observation public in local chat. This will accomplish two applaudable things: the 40+ year old women will become more likely to accept your offer to rez a prim child with them at your "home", the troll will ignore your accusation--commenting on your mother or sexual preference instead (which basically means you were right!...or else he would have argued it!).
NOTE: If you have read this far and haven't detected my sarcasm, I will be more clear: I am being sarcastic. In fact, at this point you have basically volunteered to reserve an hour or more of your time to defending you prim baby/pets/home, RL mom, sexual preferences, and your pervy IMing ways.]
2. Once the troll's attention is on you, you should feel empowered. As well you should! You're wearing an entire outfit from Gothicatz and a ripped up, oiled skin from Unique. Nothing is more intimidating to a troll than a juiced out, freshly oiled, guido nightclub-appearel-wearing, hot-headed, 47 year old nerd from Australia or England! And by now you should have at least one or two bitter infohub locals proudly backing you up. This step isn't even a step because you already know you rule.
3. [1 hour and 45 minutes later] So some back and forth dialect has been exchanged between yourself and the troll by now--empty insults, threats, mom jokes, brash uppercuts and the like. You are still winning because you still have those bitter whores at your side, and there is no one else left at the infohub to say otherwise! You're eyes are practically bleeding from the mixture of not blinking and being on the verge of crying for over an hour, and you're computer desk is piled with all of the beer bottles that you have been bragging about drinking all day (because apparently drinking alone at your computer is not only shameless anymore, but thought highly of).
You have already reported the troll as many times as he inferred that he fucked your mother, and he is still not banned! BUGGA! But don't lose hope, there is still a solution. You will want to modify your strategy to being overly and sarcastically agreeable with the troll, and even laughing at his obscene gestures that he has been spamming the entire time. They previously pissed you off beyond belief, but now that you are laughing at them, the troll will surely be caught off guard. Either that or he will call you out for the 100 times you announced publicly that you "muted and derendered" him. Everyone knows that no one mutes anyone! But still...