You can hunt just about any game bird and varmint in California with a shotgun. Ducks, geese, dove, quail, pheasant, chukar, rabbits, pigeon, squirrels, coyote. As for the .22 - basically varmint and rabbits.
I do not know of any areas around Ventura County but if you get some BLM land maps that would be a great start. There are others on the board from your area that could probably get you started in the right direction.