The oil light always comes on when the car is in accy mode. So does the SES light and the alt light. My Rover does the same thing. The codes you listed are oxygen sensor codes, and lean condition codes, which likely are a result of the O2 sensor issue.
I'd certainly try using a heavier weight oil in it. Mine likes the Rotella 15-40. You might want to swap in a new set of O2's as well.

 

This is what I did, turns out the engine is suffering from a slipped liner. It's a project car, so how long do I have until the engine is busted?

 

How do you know it's slipped liner?

 

Yeah slipped liner is an often misdiagnosed issue and doesn't happen as often as reported... Show your work...