In Oregon can a tenant add to the rental property while living there and then remove the additional when tenant moves out?

Generally whenever a tenant adds anything permenent to the landlord's property, no it cannot be dismantled and taken with the tenant as it becomes a permanent fixture. The only time this would not come into play is if the tenant had asked the landlord prior to the additions to the property that if they moved out they could take the addition with them. This goes for the trees and plants in the yard the tenant buys and installs on the landlord's property as well as anything else the tenant added to the property. The trees, flowers, bushes, etc cannot just be dug up and taken with the tenant.

This depends on the addition. But I agree that anything permanent would become part of the property. The question is what defines permanent. More info about the nature of this addition will help us help you.

Can you define addition ? The renter can not change anything unless allowed to do so. And if it is or becomes part of the house, it would normally remain with the house.

The tenant added a wall to the outside of the carport without permission and then wanted the owner to pay for the supplies. The tenant has now received a 30 move out notice without cause (not because of this issue) and I am sure he is going to want to remove the addition. Can anyone give me the ORS code which backs up what you are saying?