Most remodel and cleanout debris can go right in. The limits come from Oregon's landfill bans and from the rules at the facilities that take your load.
The Oregon Department of Environmental Quality says it's illegal to dispose of six kinds of items at Oregon landfills. They are old vehicles, large appliances like water heaters and washers, used oil, tires, car batteries, and computers, monitors, and TVs. All of them can be recycled instead.
Hazardous waste, liquids, paint, solvents, fuel, propane tanks, and asbestos can't go in a standard dumpster either. The local transfer station takes tires and large appliances for recycling, so set them aside and mention them when you book.
Jackson County also requires every load of trash to be covered or tied down on the road, so nothing blows or spills out. If you have a question about any item, ask your account manager before it goes in.