Everything needs to be checked, point dwell, ignition timing, engine vacuum, fuel pressure, etc. First step, get a Buick Chassis manual and read the ignition and tune up sections. The oil light will come on as the engine begins to stall. Sounds like you have a low fuel level in the carburetor for one reason or another.
Where are you located? As Larry stated earlier, you may be close neighbors with one of our Buick Members. Most of us are willing to stop by and help if you are within reasonable distance. Bad gas will definitely throw your cars performance off.
The engine is stalling or beginning to stall so you lose oil pressure which lights the light. If the fuel level is low in the carburetor, G force from turning or braking is enough to uncover the jets and stall the engine.
I'm located in Scranton PA. At the moment I'm serving overseas and I just returned to duty. So it could be the choke AND accelerator pump?
Yes sir. Stumble good, raise in rpm bad , a vac leak , a vac leak your actually not leaking anything but your drawing in air , so that makes your motor lean , give a hungry motor a shot of carb cleaner it's gonna raise some rpm,