water looks muddy

i just aquired a 96 neon (2 liter- 5 speed- 120,000 miles) for FREE; of course it has its problems. the one issue that i need help with is the cooling system....... it seems oil keeps finding its way into the coolant. Before i was given the car i flushed the cooling system on it for a friend, and the coolant looked grey and was the consitenty fo runny mud. i flushed the system until nothing but clean water ran out, added water and antifreeze. she drove the car for about 2 1/2 months and noticed it was running a bit warmer than normal after a while . i checked the collant again, and again it looked muddy again. other than this the car runs like a champ- No water in the oil, no bubbling in the coolant so i dont think it the head gasket, but i could be wrong. ANY HELP WOULD BE GREAT..

More than likely it's the headgasket. Oil in the coolant is a good indicator. The radiator could be bad and just rusting out while your driving, but I would think it's the HG. It's a pretty simple fix.

Well if it is the oil, dump it out and let it sit... if you see oil definitely seperating, then as das said, it's a head gasket. But, it sounds to me like it's a good chance that the radiator is just corroded like most radiators do after a few years... try flushing it out again first, and when you add coolant and water, add a bottle of Prestone sealant and 100,000-mile radiator conditioner to it... it should seal up all the pits and slow down the radiator corrosion. The overheating could just be a bad thermostat... cheap replacement part.