Ordinary remodel debris, cleanout junk, and clean construction material are all fine. The exclusions come from California disposal rules and from the receiving landfill's gate policy.
The Olinda Alpha Landfill turns away chemically treated wood, asbestos, batteries, chemicals, paints, poisons, pesticides, contaminated soil, tires, fuels and fuel tanks, mufflers and brake linings, heavy metals, explosives, radioactive material, medical waste, and any liquid load. One prohibited item can put the whole container on the wrong side of the gate.
Orange County runs four free drop-off centers for that material, and one of them is in Anaheim at 1071 North Blue Gum Street. The collection centers take paint, cleaners, motor oil, batteries, smoke detectors, pesticides, and electronics from county residents, Tuesday through Saturday, 9 a.m. to 3 p.m. The phone number is 714-834-4000.
Tires are their own problem here, since the City doesn't collect them at the curb either. Keep them out of the container and ask your account manager where to send them.