Can my 16 year old son legally invite someone to our property after we asked them to stay away on several occasions?

Your son is not the owner of your house and has no possessory interests.  as such he is merely a guest of yours.  he is a guest and has not possessory interest as he is of the age to consent to contracts and may rightfully live out of the house.  if your son invites someone to th house that you do not wnt there, you have every right to ask the person to leave as they are not welcome.  if the person refuses to leave the property, you may call the police and ask them to come to the house and force the unwelcomed guest to leave.  your son will not be able t override this decision as be is not the title owner of the house.