I'm not an expert on this (at all); all I can offer is some very basic help.
If you're using XP, then you should install SP2. Besides the fact that it is necessary and is highly recommended, it has a very good pop blocker. I know for certain that it blocks the IE popups, so that should help you. I don't use AOL (I use Avant Browser, which has a popup blocker, along with XP SP2), so if that doesn't have a blocker (although I think it does), then switch to one that does.
You say that they've installed icons on your desktop. You may have some form of Spyware, run whatever program you usually use to deal with it (ex.: Ad-aware and Spybot). Be sure to update your definitions first!