[Doug Tatham]

There are a few possible causes. 1st let me explain the alarms.
There are two sensors, one near the oil filter and one on the cylinder head. If you have a low pressure light with the engine at idle, then the low pressure sensor on the head reads low. The sensor on the filter holder goes if the sensor reads low pressure when the engine is above 2000 RPM. When this triggers you have a beep as well. If you run the engine with too low of oil pressure you will ruin it in short time.
Assuming that the oil alarm isn't on when you first start the car and comes on once the engine get hot and the oil thins down, the quick fix will be to put in Lucas oil stabilizer. It doesn't fix anything, but it increases the viscosity of the oil so that it will run without alarming. You should be using 10w 40 oil in your engine. Check this. Changing to 20w 50 (?) oil will have the same affect as adding Lucas. It's a bandaid, not a fix.

Possible problems:
1. Clogged screen on oil pump: remove oil pan, check screen, clean.
2. Bad oil pump: replace pump. Online part price ~ $50.
3. Bad engine bearings: rebuild engine.
4. Worn crank shaft: Buy rebuilt engine.

Hopefully it's just a clogged screen, an indication would be that the alarm comes on right away rather than after idling for 10-15 minutes.
Good luck.