Most household and construction debris is fine. Oklahoma's rules on what a disposal facility may accept set the outer limits.
The state keeps hazardous, radioactive, and PCB waste out of every solid waste facility. Medical waste has to go to a facility permitted for it. Asbestos can only go to a landfill specifically approved to take it, so an older home project needs planning before demolition starts.
The everyday exclusions apply too. Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
Two more items are worth flagging locally. Tires and appliances usually carry separate handling charges, so tell us if you have them. Oklahoma also limits construction and demolition landfills to construction debris alone, which is another reason to keep building material and household trash apart.
If an item seems borderline, your account manager can check before you load it.