I have a 96 A6 that I'm trying to save. A non-Audi shop says I have massive engine problems and junk the care. The following codes come up:
(anybody near chicago or west suburbs that can look at?)

P0116 Coolant Temp Sensor Out of Range
P1101 Unknown
P1106 unknown
P0401 insufficient EGR Flow detected
P0170 Fuel trim malfunction bank #1
P0173 Fuel trim malfunction bank #2
P0171 System too lean bank #1
P0174 System too lean bank #2
P1250 Undocumented Code
P0301 Misfire Cylinder #1 Detected
P0302 Misfire Cylinder #2 Detected
P0303 Misfire Cylinder #3 Detected

But technically I should replace (or clean) the MAF sensor.
"System too lean" is not good. You can easely overheat the engine. Try to replace fuel filter (if it is old) and clean codes. If it comes again - then check injectors, pump, lines.
"Misfire" - replace spark plugs if old and check spark plug wires,

Dude, it sounds, that you did not tune up your engine for long time.

P1101 = O2 Sensor Circ., Bank 1, Sensor 1 Voltage too Low/Air Leak

P1106 = O2 Sensor Circ., Bank 2, Sensor 1 Voltage too Low/Air Leak

P1250 = Fuel Level Too Low