Hi! I too have an Audio 100 Avant 1986.
With similar problem. It has happened three of four times the last couple of years.
Twice when it was very hot outside, humidity high. The engine just dies and does not want to start. We waited half a day, then it started like nothing ever happened!
Then at Winter 2 years ago, I had to drive with choke on all the time, else it would stall when I idled the throttle.
That problem was the vacuum-"hose" that was cracked and leaked. When that thing was replaced, like $30 for work etc it worked allright again!
But now, and today, the car started to go unsmooth, I thought it was my bad balanced wheels, but just as I went uphill and in a right corner the engine just died.
Just when the car stopped a "new" warning sound I have never heard before sounded.
A high-pitched beep.
Got a friend to tow me and I tried putting 3rd or 4th gear in to start. Lights went on, everything looked good. As soon as I put neutral in, that warning sound again for 1 or 2 seconds, then engine died. I think the oil warning lamp is the first to light as the sound comes, then the usual battery etc lamps start to blink.
The car now is in a sunny parking lot, and I'll try to start it after a few hours.
Just one week ago I had the oil changed on it, do you think that might be a part of the problem? Like if a sensor has been broken or oil levels are even out and the sensor needs more oil?
Is there a warningsystem in such an old Audi that prevents engine to start if some level or some system is faulty?
How did you fix your Audi, Ostrich?
By the way, I live in Sweden too.