I can't reproduce any diagonal movement of the board outline. What have you selected when you operate the arrow keys? Nothing? Board outline? One of the copper areas?

Had the outline imported as .dxf but I don't have the file on this PC. Will try later again and upload the dxf.

Added the Strainrelief.dxf If the project is closed and easyEDA restarted it doesn't move diagonal. If it is imported from the dxf it moves indeed diagonal.

that is because of the object will follow the grid to snap first

That  would be expected and should only happen once but I can move it as far as I want diagonally in all directions.

@Xenons, @UserSupport, I can confirm that when the dxf file is imported and selected but before the PCB is saved, closed and reopened, the imported shape moves diagonally instead of vertically or horizontally when the arrow keys are pressed. The diagonal movement is not a simple rotation of the arrow key direction by some fixed factor.