Oil in Radiator since mar-2007

Hello

Make - Toyoto
Model - Corolla
Year - 1996
Odometer - Approx 148500
Strange Sounds or Smell - Nil
Fluid Leak - Nothing so far
Past Repair History - Timing belt changed @90k miles, regular maintenance
Vibration - Yes when at Stop, one Engine mount (left) was found cracked and replaced. Vibration continues, advised to change all of them

The service advisor noticed oil in the radiator and did a block testing of the engine; The color of the fluid did not change (no gas leak? I am no mechanic); His suggestion was to change the radiator and hoses and do a flush of the coolant. How about crack in the head cylinder.
Showed to another mechanic recently and he vouches that this is due to head gasket leak and he said there are three possibilities depending on where the leak is (i remember two) 1. Can lead to smoke in exhaust, 2. Oil in the radiator ; He says this is common for toyoto corollas in the 150K - 180K range.
I am totally confused which one to listen to.
The radiator holds the pressure well and I did the flush once; Some amout of oil was seen again after few days. Probably the first technician was wrong.

The second technician said even oil change will be a waste of money till the problem is addressed. The vehicle has been running fine and the engine is not heating up. Now my oil change will be due in another month or so.

Fixing the head gasket will cost anything upto $800 to $1000. I don't mind spending as long as result can be seen at the end.

Please advise.

Thanks