Answer. There is nothing in the Oregon landlord-tenant laws that addresses this subject. This is not like an adult who wants to be approved as a resident and move in to an existing home. In that case, I can see that you would want to run him through the fully battery of checks.
But in this case, what would you learn? You would not be able to get any juvenile records. He probably has no credit to speak of, and his income is not necessary for establishing that his parents can afford to live in the community. It strikes me that going forward, you retain the same control over him as any other adults in the park. He has to obey the rules, etc., and if he doesn'tyou could issue a 30-day notice to the parents about his conduct.
If you wanted to add him as a Temporary Occupant, you could do that. If he violated rules, etc., you could terminate his right to be a Temporary Occupant, and require that he vacate. However, in this case, it does not seem that there is cause for concern.
If he had been a problem child, and now had grown into a problem adult, I would strongly recommend that you use a Temporary Occupancy Agreement. Your options in requiring that he vacate upon breach of the rules, are much swifter, although you cannot terminate without cause.
Although I don't believe I've seen this issue addressed in park rules, it's not a bad idea to have something in place. You could say that all children remaining in the park after their 18th birthday, must do X, Y, and Z. That way, when it happens, you will not be accused of picking on one particular tenant's son or daughter.
Lastly, I've often seen a similar situation, where the child moves away after his or her 18th birthday, and then returns a year or so later. Some landlords treat this as they would any other third party wanting to move into an existing resident's home. While it would be nice if the situation was addressed in the community rules, I have not seen this. I believe I would treat any adult wanting to share space with other residents, even parents, the same way I would treat unrelated parties; they must at least pass a background check. The rule should be the same for two residents who have been approved, then one leaves and comes back a year or so later.
In all cases, you can use the Occupancy Agreement, assuming the person passes their background check. If there is ever any doubt about the boomerang child, or former tenant coming back into the community, your best alternative (other than saying "No" based upon the background check) is to use the Temporary Occupancy Agreement. However, never let the Temporary Occupancy Agreement be perpetual; be sure to have an expiration date on the term. You can always renew it if they behave.
 The statute is here. Note that you cannot qualify the Temporary Occupant based upon finances, since it is presumed their income is not necessary for the existing tenant(s) to pay the monthly space rent.