Answer: Much depends on your rules and rental agreement, which you've not addressed. For purposes of my response, I will assume that one or both of these documents require that if a resident wants to have a person live with them at the home, they must so notify the landlord, get a background check and have management approval. If they are going to go onto the lease, then their credit record becomes important, and they would have to provide financial information as well. If the person will not be living there as a resident, then they could enter into a temporary occupancy agreement under ORS 90.275.
However, in your case, assuming that this person is actually a pedophile with a criminal record, he is not someone you want in the community under any circumstances. If he was a resident who signed a rental agreement or lease, Oregon law provides that you may terminate it by giving him not less than 30 days' notice if he is classified as a level three sex offender under ORS181.800 (Risk assessment tool) (3) or is determined to be a predatory sex offender under ORS 181.838 (Juvenile predatory sex offender defined). (See, 90.630(1)(c).
However, this person is a visitor/guest - you are not legally obligated to permit him in the community if he poses a threat to other persons, or interrupts their peaceful enjoyment. You certainly do not have to give 30-days' notice for him to vacate.
You should promptly contact the mother and tell her that the son must leave. If you are willing to give him a short period of time to find other living arrangements, make sure that he is not loitering around the community. If this is a family park, I would not permit him much more than three days to be gone. He should be warned not to come back. If he and his mother want to visit, it must be outside the community.
If the mother refuses to cooperate, you should contact the local police, and ask them what protocol they would like to you follow to have him removed as a trespasser. In most cases, you would first issue him a written notice (with copy to the mother) informing him that he is not welcomed in the community, and if he comes back after a certain date, you will call the police and have him removed as a trespasser.
Hopefully, this will resolve the matter. If it does not, either because he is seen still coming back into the community, you may have to issue the mother a 30-day notice under ORS 90.630 for violating the rules and/or rental agreement. The rule that would likely apply would prohibit persons from staying in homes as occupants or guests without landlord approval. In such case, you would have to issue her a 30-day notice for cause.
Lastly, until this matter is resolved, I don't recommend accepting rent from the mother (or son). If she pays, return it within ten (10) days after receipt. See, ORS 9i0.412(3)(a).