Lumber, drywall, roofing shingles, flooring, cabinets, doors, fixtures, furniture, and general cleanout debris are all fine in a roll-off container.
Oregon publishes no single statewide banned-materials table, so the real limits here come from Metro, and Metro's refusal list is specific. It will not take asbestos-containing material, burned material or wildfire ash, flat or built-up roofing, loads of liquids, petroleum-contaminated soil, radioactive metals, electric vehicle batteries, or vehicles. Metro adds a warning with teeth: customers are responsible for items left at its stations and can be fined or charged the cost of asbestos testing and removal, with those costs able to exceed $3,000.
Household hazardous material stays out as a matter of course. Paint, solvents, fuel, motor oil, antifreeze, pool chemicals, pesticides, batteries, and fluorescent lamps all need a hazardous waste route rather than a container, and Metro runs separate hazardous waste hours for exactly that.
Asbestos deserves the extra sentence. Tualatin has a large stock of 1970s and 1980s housing and commercial building, which is late enough that asbestos is less common than in older cities but early enough that it still appears in floor tile, adhesive, and pipe lagging. A survey before demolition is cheaper than a refused load and an asbestos testing bill.
Anything out of the ordinary is worth naming at booking, and the separate route for it is arranged beside the container.