Intake and head gasket leaks will not cause oil in the coolant.
A leaking oil cooler in the radiator end tank will cause oil in the coolant. No question. That is what it is.
Follow the oil cooler lines from the oil filter adapter at the oil filter. They go to the end tank of the radiator. You can remove the radiator from the car, unbend the tangs that crimp the end tank in place and remove the end tank. That will allow you to remove the oil cooler in the end tank and replace it.
If the car is just driven locally and never used for towing or anything it is fine to disconnect or bypass the oil cooler if you want to for a beater. Just cut the oil cooler lines/hoses near the radiator fittings and hook then together to bypass the cooler. Use a piece of tubing and clamps. If you do this, use double clamps and safety wire the clamps together the keep the hoses from pushing apart when the oil pressure is high on cold starts.
It is perfectly fine to run without the cooler. The oils since the engine was engineered for 1992 have improved considerably and will easily handle the normal operating temperature of the 4.9 unless you are doing some heavy duty driving such as towing or continuous hill climbing in a hot ambient.
Use the 15W40 Delo/Delvac/Rotella oils in it and it will be fine without the cooler.
You should take care of this ASAP as likely coolant is getting into the oil but you don't see it. That will happen when the system is shut down and the hot (pressurized) radiator pushes coolant into the oil side of the cooler. This has the effect of depleting the oil and causing potentially severe engine wear.
I would bypass the cooler or replace it and change the oil immediately. Use the heavy duty oil mentioned and add a pint of GM EOS (engine oil supplement) available at any GM dealer to spike the oil with the ZDP antiwear additives to prevent any further scuffing or wear that may have started. Don't delay and don't bypass the oil change and EOS addition.
