Almost all renovation debris is acceptable. Lumber, drywall, plaster, roofing, flooring, cabinets, doors, windows, fixtures, furniture and general cleanout material all load without difficulty.
Nothing hazardous rides in an Oak Park container, and nor do liquids, paint, solvents, fuel or asbestos. Asbestos matters more than usual on Oak Park's older housing stock, where it can turn up in floor tile, pipe wrap and siding, so get it tested and abated separately before any demolition starts.
Two local limits are worth knowing. The transfer station that receives Oak Park loads takes no yard waste at all, and the authority that runs it accepts no brush, branches or woody tree material at any of its sites, so a tree job needs a separate arrangement. The city code separately bars concrete and dirt from any waste receptacle put out for collection, along with poisons, ammunition, explosives and anything hot enough to ignite the rest of the load. Liquids are only acceptable when sealed.
Tires, appliances and electronics are generally priced by the piece rather than by the ton at the Troy station, so stack them to one side and name them at booking.
If you are holding something and wondering, that is the moment to ask your account manager rather than after the container is loaded.