it is legal to ride on the road if you have full registration. to get the full reg. you need the following: stop/tail light headlight mirrors indicators horn. but there might be a cc restriction. with full reg and license you can ride anywhere.
It is legal to operate pocket bikes in the state of California. The only state that it is illegal to operate pocket bikes is the state of Florida. If the pocket bike is under 100cc ,it is okay. Pocket bikes are not considered motor vehicles in the state of California.