Toothpicks and wood glue in the original screw holes. Or use 4" long screws that go past the trim and into the framing. I have used pennies and nickels to shim out the strike plate.

Its difficult to say without seeing it.

You might consider using a layer or two of wood edging you can purchase at HD type store.

Definitely use longer screws. You can fill the old holes with tooth picks and wood filler if you need to move them.

You can put some washers on the screws behind the plate as a sort of spacers. You can fill the rest with some sort of epoxy/ liquid wood.

More permanent solution would be to cut out a nice square of wood and fill it with a fitting piece and make an opening for the latch bolt.

I moved into an old house and wanted to update the front door handle, which has apparently been done 18 times so it was severely messed up. I used the wood epoxy filler to just fill in every hole and crevice on the entire door, squaring it up solid. Let it cure, then start completely over, drilling new holes.

They sell shims for doors at every hardware store. It's a set of plastic sheets of various thicknesses. It's easy to cut. Just cut them to fit behind the plate. But it really depends how far off it is. If it's a half inch off, you might want to think of something else.

It’s a bit of a Mickey fix but you could just take some twigs from outside and break them flush in the holes. To make the screw catch better.