2002 Jetta 1.8T random oil pressure warnings

indicates a problem oil pressure sender unit
have the oil pressure checked using a mechanical pressure gauge and if OK then replace the sender unit or gauge

The oil warning light has nothing to do with oil level. That is not the way this warning system works. The warning light comes on when the oil PRESSURE drops too low as determined by an oil pressure switch installed on the engine. So you could have low oil on the dip stick but still have enough oil to maintain oil pressure in the engine. It is also possible that the oil pressure sensor is faulty. This probably is not connected to the vehicle cutting out when passing the truck. That could be something as simple as a dirty fuel filter or clogged injector. Since you are losing oil there are a variety of problems that your engine could be having.

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Get it in for diagnostics, the possibilities are endless, but do not drive the car!
A) Check the oil levels, and if there are any leaks
B) Check oil pressure sensor

When last was an oil change service done?

Did you compare what your dash gauge read when it was acting up and compare it to the manual gauge at the same time? I know you said you used the manual gauge and it read fine so if you get a proper reading out of the manual gauge and an improper reading out of the dash gauge then your dash gauge needs addressed.

It might be a bad oil pressure sender.Take car to a garage and have them test the engine oil pressure with a mecanical oil pressure gauge.I would not drive to much because IF oil pressure is down you might loose the engine

This could be warning you of dangerously low oil pressure , which could damage your engine , or perhaps the oil pressure sender unit is not working. It is an inexpensive part , and easy to install.
Do you have any other issues ( warning lights etc. ) or gauges that aren't working.? Together they could indicate an entirely different problem. If you need further assistance please let me know thanks, Midwest-tek

I would check for the wire that comes off of the oil pressure sensor if it get grounded it will turn the light on
when you eccelerate that shift the motor and could have rubed the wire some where

Take it to the dealer, the EPC warning light - and even more the failsafe run which doesn't allow you drive faster than 20mph) is an indication of serious motor troubles. They can read the ECU faultcodes, which should be a good startingpoint for troubleshooting the cause ...

You could do some basic troubleshooting like checking the air filter, the oil level, the spark plugs, etc. You didn't fill it up with bad gas, did you ? And does the engine make strange noises/vibration when running idle ? In case you fixed some obvious cause, you can dis- and reconnect the battery to erase the engine's faultcode. If it's not fixed, the EPC (and failsafe run) will simply come on again.

My advice would be not to drive it untill it's fixed to prevent more potential damage.

my 95 vw jetta oil light is on and there is a beeping sound what might be wrong

That's the motor-management warning light. Meaning: serious errors are being detected by the motor-management computer (= ECU). You should have a dealer readout those ECU faultcodes using VAGCOM to determine the cause a.s.a.p, before (more) harm is done to the engine.

Please be aware that your motor could also switch to "failsafe" mode when too many severe errors are detected, meaning it's terribly slow to drive and turbo-pressure is nearly non-existing.