I have a really bad oil leak. What could be wrong?

Those A5 trannies are junk and can set the vehicle on fire in less than 5 minutes with low fluid. Red fluid is tranny, oil is oil. Rear seal-oil- big repair. Tranny coolant pipes-Tranny fluid-small repair. Replace filter, fluid, and gasket-it's probably over due-and check again for leaks. rear tranny seal leak, average size job.. Never use the stop leak! Throwing flour on the tranny works better-Just kidding.

it could leak oil to youre exaust pipe

Check the oil pressure switch first, just have the car idleing & watch the switch to see if its leaking. if not look for the clean part as a bad oil leak will wash the motor where it is leaking. common mistake people make when diagnosing oil leaks is to look for the dirty parts but you need to look for the clean part.

The O2 sensors last about 100k miles on this car. If they are that old, they are due for replacement. Failing O2 sensors will set a computer code (not necessarily the code for the O2 sensors) but will not cause the car to fail to start. The car does not need O2 sensors to start.
Oil gets burned. A valve cover leak above the exhaust manifold may cause the oil to burn on the manifold and never make it to the ground. You can smell that happening.
Oil can burn in the engine because it is leaking past the valve stem seals (bad) or past the piston rings (really bad) or it can get pulled into the intake manifold through the PVC system if the PVC system is gunked up (a pain to clean out, but not really bad).
If your oil consumption is less than a quart every 1000 miles, it is annoying, but not really a problem. If it is more than that, there may be repairs in your future. Perhaps very expensive repairs.

pull the oil dipstick if there is only oil then uncle is wrong. if you overheated it really bad then it could be that though. depending on the mileage and service done already it could be the starter or timing belt failure.

It most likely got the gasket hot or vi berated it loose also look at oil sending switch by distributor

Could be just the OIL COOLER. VW IS CORRECT.
If the oil cooloer fails internely you will have a mix of coolant and oil. In the engine and in the Radiator,

But not to say the other guys were wrong...

Go get a second opinion. A bad head gasket shouldn't cause an external oil leak (unless it is really bad and you are using quarts of oil a week). If anything, I suspect it maybe a vavle cover gasket causing oil on the engine.

First of all check the cap and the dipstick. If they are intact then you need to degrease the engine and fill with oil. Then look while the engine irunning where the oil is leaking from before you know what is wrong. I hope this helps.

did you overheat the vehicle?..if oil is on one plug severely you may have mechanical issue (rings/valve stems) leaking into cylinder...get diagnostic compression test and leak down and scope electrical secondary system and advise me results