Hello. I live in an old house, built around 1880. The previous owners
repaired and renovated extensively, but nothing in the house is square.
The interior doors do not latch, or even stick closed. As far as I
can tell, there are two reasons for this.

First, as I said before, nothing is square. Most of the doors (big,
heavy, 8' tall solid wood) don't even reach the strike plate... they're
off by 1/4" or more. I have a feeling that none of the doors are
matched with their original frames, and perhaps the components of the
frames may have been mixed and matched.

The second problem is that the doors are loose. By this, I mean that I
can lift up on the free end of the door a little bit. This movement
seems to come from within the hinge. The hinges otherwise seem to be
secu they are screwed in tightly to both the jamb and the door.

So it seems like I have my work cut out for me if I want doors that
shut all the way. Short of tearing out the frames and rehanging them
properly and then repairing damage to the surrounding wall, is there
anything I can do? I was thinking about attaching a 1/8"-1/4" thick
strip of wood to the inside of the frame to fill the gap. It seems
like this might work until I can hire someone to really fix it. I
thought I would check here for any good advice or alternate solutions.

I'm not too worried about maintainin historical integrity, if there's
any left. However, new prehung doors would look out of place.

Thanks for reading.

Joseph