I would pray. Just Ask God to clense your home of any unpure spirit or feelings. When you pray, pray with your son, and you have to really mean it. Teach him to pray if he is scared. Also, play uplifting music, don't read or watch anything that would invite any bad feelings, or spirits into the home. Always have your home a place of peace and a haven for the kids.
I had an experience with soemthing I'd call spiritual in nature. I do not believe in ghosts in the term that the world or hollywood views them. I believe that there are spirits from God and Spirtits from Satan. I Believe that if either are there they were invited. By invited I mean by actions/music/atmosphere, NOT as in a seance or anything weird like that. I believe that the feeling in the home, the way people think (pure thought vs. evil thoughts) CAN have an effect on the veil between our world and the spirit world. I DO NOT beleive they can harm anyone though, but they can be suggestive, as in place feelings or thoughts in your mind.
Don't feed his spirit theory, you don't want to spook him. Just do as you did, aknowledge his concern, tell him you unterstand his feelings, if youdo, and ask him when he think woudl be a good idea to make them go away, soemtimes kids have GREAT ideas. If he has none, ask if he woudl like you to pray with him, or read him an uplifting story before bed, and play soft happy music in his room.
My son has some really bad nightmares every night for about a month, and when we took him to the school counsler, she said for us to ask him what a good solution would be. He said maybe he could make a dream catcher, So, we made one together, and he has not had the problem since. I don't believe in the dream catcher, but HE DID, and his idea was his way of fighting his problem. It gave him a chance to be a problem solver too.
Good luck.