What can cause gas an oil to mix

Could have a bad injector allowing fuel into the oil. Either that or a bad fuel pressure regulator. You need this confirmed as the engine miss is a big clue as to what injector may be malfunctioning.

Roy

You need a fuel pressure testor, voltmeter and test light. If you have never done this before, I suggest letting a shop verify it for you

Roy

Turn the key on and see the pressure. Should be around 55-60. Turn the key off and it should remain there or a little lower. If it drops off to 0 then you have a bad injector. By pulling the code for the check light, it will tell you the cylinder for the bad injector.

Roy

This is a Vortec engine and the injectors are not accessible from the outside. Beside a leaking injector, it's very common to have a leaking regulator or line that will give you the same result.