Portland Oregon City Code:

14.20.070 Advertising on Streets.
A. It is unlawful for any person to scatter notices or advertisements on any street right-of-way or to post a notice or advertisement anywhere on a street right-of-way or upon the exterior of a public building.

The penalty is $1000/sign.

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And in unincorporated areas in the state:

State of Oregon Statutes:
368.942 Posting notices, signs or pictures on structures within county road right of way prohibited. Except as provided in ORS 368.950, no person may paste, paint, brand or in any manner whatever place or attach to any building, fence, gate, bridge, tree, rock, board, structure or anything whatever within the limits of the right of way of any county road any written, printed or painted advertisement, bill, notice, sign, picture, card or poster, except within the limits of any incorporated city through which the county road
runs. <1973 c.462 s.2>

368.990 Penalties. (2) Violation of ORS 368.942 is punishable, upon conviction, for each violation by a fine of not more than $100 or imprisonment in the county jail for not more than 30 days or both.