Not only resulting from noisy supply currents, but also from ground return currents of clock signal running back from micro to oscillator modul!
It's better to use the internal Pierce oscillator of micro in combination with this obligatory quartz.

Wow, I didn't know that, I always thought an external oscillator is a superior solution in all respects...

the above from Kai is not necessarily totally correct. While the statement per se is correct, a correct layout of the board will eliminate the "ground return currents" and an external oscillator will not have any adverse effect. Since it is a rarity for me to have only one processor on a board, I use external oscillators extensively and, yes, you need to know what you are doing with clock signals.

Is there an explanation, why the external oscillator is more "dirty" than the internal one? Does it have bigger power consumption, or is that the HF ground return "common resistance" which makes it "dirty", or what?
see above.

Now to Mahmood: I absolutotally agree with the "one layer will not suffice" but looking at your pictures, it seems you have committed a one layer cardinal sin. I do not see the ground traces being any heavier than the signal traces. Now, this is not "try heavier ground traces before going multilayer", by no means, but would have reduced your problem, albeit, I guess, not significantly enough. In other one layer cases it might have.

Now, I would go one step beyond: go 4 layer. with 4 layers, you can do magic with separating analog and digital ground.

Erik