I noticed on my 2003 S80 that the housing for the 7506 bulb is twisted such that I can't insert a bulb into it.

Is it like that on all cars or my car has a problem? (I bought it used)

I also made all posision light bulbs the same and still I get the dreaded "positionlight bulb failure" indication

 

You did replace 4 bulbs correct?

 

Yes!
But none of them is the 7506.
Is it needed on both sides? now I have it only on the left and can't install it on the right.

 

Which bulb is that for?

If it is for the rear fog light they only come with one from the factory.
Also some of the bulbs on the S80 have offset pins.

 

I swapped all those weird euro number bulbs out with standard 1156 and 1157 bulbs. The pins and watts are the same.