Two thoughts:
Where you have
delay(20);
gomb_megnyomva = gomb_bekeres();
if(elozo_gomb != gomb_megnyomva)
That should be
if(elozo_gomb == gomb_megnyomva)
You have waited 20ms, and you want to see if the value is now stable. If it's stable (not changing) then you are sure which button is pressed, and you will continue. The previous if() should stay as != though.
The other thought is calibration. The number ranges selected are fairly narrow. The tolerance of each resistor means it might be slightly different to the next person. Have you checked that the input values are correct?
Also, confirm the output values.
You could modify your code so that if (r>=800 && r<=1050) return(VOL_DN)
This will make all buttons do volume down, but then you know if the volume down output level is correct, and the whole program and circuit is basically working.
You could also put an LED with load resistor on another output, and set that pin output = (r>800 && r<1050) so the LED lights up whenever you're pushing buttons.