Oak (and waxed) furniture over-sprayed with car-paint. How to restore?
Self answering to tell you about the results.  

I started on the backpanel (which is normally out of sight so ideal for testing)  with 3 different paint-stripper products to see which one would work best with this paint.
Used paint-stripper specifically for car-paint, regular household paint-stripper (both from the DIY store, made by Alabastine). And I tried a 20% solution of dichloromethane which I had leftover from an earlier project.  

All 3 worked pretty well, but the regular Alabastine stuff got the paint of better, without the need to really scrape at the residue. (Given the fine detail in some places on the furniture I really wanted to avoid scraping/heavy sanding if at all possible.)
Some remnant stuck, especially where the underlying wax had been very thin or worn away. But from the test with dichloromethane I noticed that that stuff had worked exceptionally well in similar spots.
So I tried dichloromethane as a 2nd application to those spots where the Alabastine hadn't entirely worked. That turned out to work great and got nearly everything off.  

So I ended up with making to passes: First the Alabastine and then the dichloromethane.
I then gently warmed the wood with a heat-gun and used a rag soaked in methylated spirits to draw out the remaining wax. Had to do that 2 or 3 times to really bring the wood back to its raw state. This also opened up the grain of the wood which I considered a good preparation for the new layer of wax I wanted to apply later.  

The end result was quite good. Here and there a small amount of paint was left stuck in a deep scratch, but I could carefully scrape those out with the point of a knife.
A sanding with fine wire-wool smoothed the wood, without destroying any fine detail on the woodwork.
The wood ended up a bit uneven in coloring, but I will be able to smooth that out with colored wax when I re-wax the furniture later this week.

All in all it was far less of a nightmare than I originally expected. I am guessing the wax underneath the paint was my savior. If the paint had gone straight on the wood, it would have been much more difficult to get off.