Most remodeling, roofing, and cleanout debris can go in your container. Ohio law and the disposal sites set the limits.
Ohio has banned lead-acid batteries from landfills since 2008, according to Ohio EPA. That covers batteries from cars, boats, motorcycles, and similar vehicles. Stores that sell new ones must take your old battery back for recycling.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster either. The same goes for gas cylinders and unknown tanks.
For household chemicals, electronics, and appliances, Trumbull County residents have a free option through the Geauga-Trumbull Solid Waste Management District, covered in the next section. Pull those items out before loading so your container isn't turned away.
If anything on your list is in doubt, ask your account manager before it goes in.