I am guessing here, but 2 issues come to mind. Valve seals on an old engine and a turbo seal.

First is to warm up the engine and check the crankcase pressure. Do this by pulling out the dipstick and placing a finger of a latex glove over the dipstick. If the finger gets drawn in, good, or if it gives you the bird, bad. If you get positive pressure, you will need to clean out the PTC nipple on the air intake (between the air cleaner and the turbo). It is also possible that some of the other vacuum hoses are clogged and need to be checked/replaced. Dealers just do not make these checks.

You could remove the bottom hose to the intercooler and check for oil, lots of it. That is what happens to old turbos, the turbo seals are replaceable, but you need a serious workbench and tools. I can point you to a procedure listed on a British web site, but there are probably others based in the USA.

Valve seals do wear out and excessive crank pressure will push oil past the seals. This is not a 'minor' fix and most of us drive with the problem, removing the head and replacing 20 seals is not for the normal gear head. If the seals get bad enough, you will find that long warm up times will generate blue smoke out of the exhaust as will long down hill stretches of road.

Yes, burning oil will coat the O2 sensors and make them produce codes.