Check the stickied OC PAMPHLET thread (first thread in the Oregon forum) for a lot of good info and then do your own research of the Oregon Revised Statutes. The ones that apply to firearms are 166.170 to 166.380. Not a lot of reading like some states.
Portland is unlikely to issue you a non resident CHL. Grant County is the bet bet though it is a ways "out there" and unlikely to work for you. Not sure but they may be able to coordinate with your local sheriffs department and get you a CHL via mail with the local SO's assistance. That's probably a long shot.
Open Carry in Oregon without a CHL is legal except in/on "public buildings" (as defined by ORS 166.360) but local ordinances can regulate that the weapon be UNLOADED. As far as I know there are no counties with such regulations (but check for yourself). Most of the state is fine for loaded open carry and those that regulate it you can carry unloaded with your loaded magazines (or speed loaders) on your side, just not in or attached to the weapon. Be cautious though as a couple of localities attempt to regulate that magazines must also be empty.
I would recommend reading the ORS, starting with 166.170 and then looking up all the city and county regulations on the web as well.