iI accidently put a little less than a quart of oil in my radiator and ran it.

No, the oil you put in radiator has nothing to do with,the fan.To fix your problem all you have to do is undo your drain on radiator,run water in radiator,and let car run for about ten minutes,keep close eye on the water going in and out,but it will help flush it out,now for the other fan not running,one fan run,s ac,other run,s as car temp rise,s,,it should cut on when car heat,s up,if not may be bad temp,fuse, sensor or fan motor.

Thanks. I figured the fan was something completely different. I've actually already done exactly what you suggested. Drained it, flushed it with water, and then filled it with water. Ran it for about ten minutes and then repeated the process. Done this 3 times now but the gunk is still visible when I open the radiator cap. Read on other sites possibly using simple green or certain types of soaps/detergents. They didn't say if I should let the car run with these products in it so I have decided not to. Was thinking about getting some sort of coolant degreaser tomorrow at an auto parts store. I have to travel about 150 miles tomorrow but I want to make sure that I don't overheat my car or make matters worse by driving with that sludge still in the radiator.

No do not use detergent or any other cleaner in radiator,it will eat it from the inside,aluminum,they have radiator flush cleaner at auto store,

Yeah I had a feeling. So in the morning I will buy a radiator flush cleaner at an auto store. Do you have any recommendations on which one I should purchase?