Should I use longer screws or cardboard shims for fixing skewed doors?
Cardboard shims have been a long time fix for door hinges to adjust the gap. Make sure first the screws are still holding. If they have gotten loose then it may only need tightening or perhaps filling the old hole with carved dowels and resetting the original screws to get the door to draw back in place. You may use longer screws to accomplish the same thing.

Another issue with houses over time is the floor framing shrinks or sags over the span and the door will not line up at the strike because of the jamb has lowered on one side more than the other. To fix this will take more than resetting screws or adding shims behind the hinge.

I can write more on this type of fix if you find that may be the case.