Read ORS 166.170 to 166.380
Without a CHL you can open carry a loaded weapon EXCEPT:
In "public building" (as defined in the regulations which the listed sections will point you to);
In cities or counties with a prohibition on loaded open carry (they are not allowed to regulate unloaded carry)
You should check the stickied threads (only two) in the Oregon forum and download the Open Carry Pamphlet as well as read up on the ban cities. THEN you should check the specific cities through which you will be traveling to determine the status of each jurisdictions regulations on loaded open carry.
I am not a lawyer and you should never take legal advice from anyone other than a lawyer with whom you have an established client relationship (including a consultation), read the regulations personally and understand them.
Keeping your weapon unloaded and locked in a locked weapons box in your trailer should be perfectly good throughout Oregon. The only issue would be loading it and carry (even within the vehicle) if you are within a loaded carry ban city.