I have a 2000 Oldsmobile silhouette which is pretty much the exact same van. I had the exact same problem. The brake lights, turn signals and taillights all worked fine as long as you only used them one at a time, but if you hit the brakes with your signal on, or signaled with the taillights on everything went nuts.
It was also having a problem where it was shutting off the traction control system.
I took it to a shop and it cost me about $800 to have it all fixed. Most of that cost was labor to find the problems and install new parts, but there were about $150 worth of new parts. There was a pigtail connector in the brake light assembly that was fried, there was a sensor on the braking system that was broken (which was the problem with the TCS) and there was one other electrical component that was broken (can't remember what it was called).
Good luck, you probably need to take it to a shop that does electrical work, and be prepared to pay