I got this 1991 cavalier and have never ever changed out the coolant, so I decide to completly clean out and flush the system. The only problem I'm having is trying to clean the overflow tank. I washed it out with water but cant get this black buildup cleaned off the the inside of the tank with plain water. Is there anyway to clean this off with some special cleaner or technique?

you could try to add some ammonia in the water, and take the overflow tank out, cap the ends and shake the shit out of it to try to get the sludge loosened up.

I cleaned one recently by removing it and running hot water and brake cleaner through it. Cleaned it to showroom quality, but I couldn't get the brake cleaner smell out of it - even with repeated clear water flushes afterwards...