Hi fzabkar,
thank you very much for your reply!
They could be low capacitance ESD protection diodes. If you remove them, I expect that the device will work without them.
Yes this was my guess, too, but they could also be some MOVs (TVS or ESD). I de-soldered them and soldered three micro dip-switches on the board. When I open all three switches the open-calibration passes and when I close them all the short-calibration passes, too (having the shorting bar installed of course). All other dip-switch settings give a fail in calibration. Unfortunately the meter still jumps around some weird values, even after successful calibration. What is also interesting is that if I close all switches and test a small cap the meter shows an overload and if I open all three switches having the cap still installed the meter shows the correct value of the cap (without jumping around)!
I couldn't find anything in the datasheet ...
Me either. I checked all the public Cyrustek documents. But the helpful stuff (e.g. pinouts, schematics, chip internals ...) seem to be top secret for this particular chip. I had great hope in this post by Hydrawerk
And here is Appa 703 internal circuitry. https://plus.google.com/photos/104378593109746079667/albums/5601643946056628337?sqi&sqsi
... but the link is dead (and Google Plus is, too). The original schematics of the meter would have been most helpful.

Is there an ESD1 and ESD2? If so, see if they test like zeners.
Good idea, but they seemed to have seen the magic smoke, too (they protected the USB port). All of them behave like 0 Ohm resistors. No capacitance, no inductance, no resistance whatsoever. Really strange ...
Thanks again for your help!