My son's mother moved out with my son without any advanced notice. Am I entitled as the owner of the items that she has left in my house?

You own your items in the home, and after you file in court and get custody of the child, the child's items would stay with you.

Items of the babies mamma ( I assume not your wife) still belong to her and she needs to be notified to get her belongings.

At this point you need to file for cusody of your child in court