How do I rehang a wooden door with worn screw holes?
A few suggestions:


Are you using a wood glue such as Elmer's to hold the toothpicks in place?  The top hinge on my front door used to pull loose; I repaired it with toothpicks and wood glue (pretty much filling the screw hole) and haven't had any problems in several years.
How long were the original screws, and what did you replace them with?  When I installed a new interior door a few months ago, I replaced the 1/2" screws that came with the door with 2 1/2" or 3" (I forget which) screws of the same thickness.  Assuming normal framing, you have two 2x4s, possibly some shims and the jamb itself, so there's plenty of wood there for a long screw to grip onto.
Take the hinge plate off the jamb (support the door so it doesn't pull the other hinges out of the jamb) and drill out the screw holes that are giving you problems; the hole should be as deep as the existing screw.  Glue a dowel of the same thickness as your drill bit into the hole.  Before you replace the hinge screw, drill a pilot hole to ensure that the screw goes in straight.