Door Does Not Close Properly
There is a way to tweak the hinges to move the door up or down, but its for small amounts like 1/16", not 1/4". It's better to just move the strike plate. However, if the door is sagging 1/4", then the top of the door must be sagging down from the header jamb and leaves a giant gap between the top of door and jamb. Also, the top edge of the door must be rubbing badly against the jamb. If this is occurring, you'll want to re-secure hinges (re-tighten all screws) and re-plumb the door. 

Best way to move strike plate is to chisel the jamb out to receive the strike plate and then reset the strike plate. I'd also cut a small piece of wood,the amount you moved the strike plate down (1/4"), and glue it into frame to match rest of frame. (Then do a little touch-up of paint or stain to match rest of frame.)

The hinge should not be loose enough to pick it up 1/4" or so. Re-screw all the hinges down tight before you move the strike plate.