Originally Posted by PhySteve

I solved the Oil Pressure issue! It was the sensor. To make it easier for people to resolve this issue I'm going to write up in more detail the symptoms, solution, and steps I took.

2003 Audi A6 C5 3.0L
Symptoms: Red Oil can light came on randomly followed by three loud beeps. The light would stay on for a period of time and turn off. Sometimes well the light was already on the three beeps would occur again signaling that the sensor had reported normal and immediately fell back and reported bad conditions.

Investigation: Oil Temperature and coolant temperature remain in normal conditions. Upon inspection oil levels were sufficient. Oil was worn but contained no visual particulate. The engine was not knocking. No indications of oil leaks were found. Normally at this stage test the oil pressure. The oil pressure check gauge can be hooked up just above the oil filter at the oil pressure sensor. The Oil pressure sensor can be removed by first removing the connector (on the front of the sensor insert a flat head screwdriver to lift the clip), and unscrewed with a 24mm deep socket. Oil will leak out.

Solution: Assuming oil pressure was within normal specifications replace the removed oil pressure sensor with a new one. Visually check the electrical connector for damage, and if applicable clean with electrical parts cleaner
.
"Solution" didn't work: At this point I would have dropped the oil pan and investigated the oil pick up tube. If the tube was clean the engine might be worn (bearings are bad) or the oil pump might be bad. At this point I would have added thicker oil and drove the car lightly until engine threw a rod. Don't be like me.