Off road you need muffler, lights, and seat belts, shoulder belts, and all seats must be inside the vehicle. On road you must be road worthy, and have legal lights, windshield, wipers, horn, mufflers/catalytic, seats and belts. Your lights need to be not glaring in traffic, and drive like a normal human bean.
As an out of state vehicle, you won't be pulled over for inspections unless you act up, or do something dangerous.
Remember too, it is HOT here, so drink your water, and stay hydrated. Some trails are being monitored for use now, as we are so dry and a fire danger is so high. NO SMOKING in open vehicles, or while moving in the forest, as again we are so dry, and stuff. I just returned from the southern Sierra's, and ALL the campgrounds were limited to Propane stoves only! NO charcoal, or NO open camp fires! You even need a fire permit now for propane stoves, and you can only camp in developed areas.
A fire permit is free, and you can get one at any forest office, or many campground hosts have them.
Carry water for drinking when off road, as well as some basic first aid stuff. Some other stuff you may want are; Tow strap, jumpers, flash lights, basic tools, duct tape, and of course.....common sense. It is easy to get quite a long ways from the nearest cell signal, and many guys use CB off road to keep in touch.