I think it's going to be difficult to find something in CA where you can drive AND camp on the beach
Gold Bluffs beach camp ground (Prairie Creek Redwoods State Park) is nice. It's a dirt road to the camp ground. The camp sites are on the edge of the beach with the redwoods to the east. If you stop here besure to check out the nearby Fern Canyon. Prairie Creek Redwood SP
Mattole Beach is a little farther south, located near Petrolia. The campsite isn't great but it is right next to the beach and it doesn't seem to get much traffic. There is a six mile hike south on the beach to an old lighthouse. Mattole Beach - Lost Coast of California
Manchester SP has a drive in campground and walk in camping on the beach, but no driving on the beach. Manchester State Park
On the map above, there is "Usal Beach" marked. You can camp right on the beach there, and there are some other campsites back in on the river and a campground. It's WAY out of the way, but a nice place and lots of wildlife. If you stay in the campground, use more than common sense when bear proofing your food supply.
As for camping, I am not sure. I know places like Sand Lake (near Tillamook) have restricted their camping areas to the designated campground.
from some googling, probably best to verify the info below with Oregon Dept. of Parks and Recreation-
"Ok, I just called the Oregon Parks and Recreation Department (800-551-6949). I was right: camping is legal, except where prohibited.
The no-no's are:
-- No camping in areas that abut state parks;
-- Not within the city limits I mentioned above;
-- and not where signs are posted prohibiting camping.
Anywhere else, within the bounds of safety, common sense, and good taste, is fair game. The person I spoke to said that they have closed down a bunch of areas where large numbers of people used to camp, due to excrement and trash issues -- this may be code for "homeless encampments" or "hippy party spots," I don't know. But if they haven't posted a sign saying "no," and you aren't next to a state park, you are legal."