Set up high definition video cameras in every room in the house.
I see 4 possible outcomes:
1: Ghosts aren't real, you'll find out you have rats in the attic and we can all stop living in the dark ages.
2: Ghosts are real but they are afraid of cameras, in which case your problems are solved as long as you keep the cameras on.
3: Ghosts are real but they are not afraid of cameras, in which case you will become a millionaire for proving the paranormal.
4: Ghosts are real but cameras tick them off and they'll destroy the cameras and kill everyone in the house.
In any case calling in some quack will, in the long run, be far more expensive than good cameras and won't get anything accomplished.