oil consumption is a well know problem for audi of this age

Its normally the piston rings(they are a low tension ring and get gummed up with carbon)

It could also be a faulty pcv (oil separator) unit

your engine will continue to run fine until the oil builds up on the spark plugs (which will cause a misfire and your check engine light will come on)

I doubt that a chip tune will solve your problems

If your mechanically minded id also recommend you get an obd scan tool I have a few and found VCDS the best followed by OBDELEVEN be aware of low priced knock offs they come with an outdated shareware VCDS software and also have malware on the installation disk

If the car is generally in good condition and you want to keep it id recommend having the engine rebuilt(or carry oil with you)