Overheating, using oil and leaking coolant

I suspect engine oil in the radiator. A dark colored film appears to be floating on surface of radiator reservoir.
The oil dipstick looks normal-doesn't appear contaminated, don't see bubbles.
Closer inspection revels coolant leaks at bottom of radiator when under pressure-have not yet identified exact location.
Engine oil level has also been low lately, indicating oil loss. No blue smoke is seen and no burnt oil odor is evident.
What diagnostic steps and tests can be performed to determine if the engine has a possible blown head gasket or is this a oil cooler/radiator problem?