How do I repair a door jamb that has soft and split wood at the hinge in my 100 year old house?
The short answer is longer screws, plus some glue.

There should be plenty of extra room for longer screws on both the door and the jamb. If the hinges are brass, solid brass screws are best.  Pre-drill. At the same time stick in a small strip of wood soaked in wood glue into each hole just to be sure.  Toothpicks, chopsticks or similar dry wood work well.

For bonus points sand off the lacquer coating on any solid brass screws you buy, so they will tarnish faster and match your hinges.