Align layers diagonally

I don't know about any possibility to do that. If you would have all layers with same dimensions then you could record action.

1) select all layers

2) align all layers to the left top corner

3) translate layer by certian value

4) select next layer

5) repaeat last transformation x-times (CTRL+SHIFT+T)

6) select next layer and repeat 5) and 6) until there are layers

This is only actionable if there is always same number of layers and all layers has same size otherwise it will show you error or it will be misplaced.

If you want, I could write sophisticated script which exactly meet your needs on order for money. I already did some scripts: http://bereza.cz/ps/

https://www.google.com/search?q=Photoshop+script+distribute+layers+along+a+path&oq=Photoshop+script+distribute+layers+along+a+path&aqs=chrome..69i57.29503j0j8&sourceid=chrome&ie=UTF-8

I am sure something like that can be scripted.  If you want to know if someone has scripted that. Searching the web may fine something like that.  Some posted scripts are very useful some do just one thing other are more flexible.  Think of what you want to do in more general terms than align layer to a diagonal and search on that. You may find something someone has programmed that you can use to do what you want. To me "align layers diagonally"   would not be a good thing to search on the are to many unknowns but is also limited not of general use the search is vague and may return to many poor hits.

Think of a search the would be more specific and something that would likely have been Programmed.  Like distribute layer along a path.

Diagonal is a path but a path can be much than a diagonal be more useful and more likely programed like text on a path,