How can I check for outstanding warrants in California, so I can go clear them up (any would be prior to 1980)?

I think it is wiser to have an attorney or investigator inquire on your behalf, especially if you are considering contacting the police - unless you are absolutely sure that any warrants are for very minor traffic tickets which carry fines only.

Other agencies to check would include DMV and the local courthouses.

You can request your driving record by:
Your DMV record is available to you during normal working hours. You may obtain a copy of your California driving license/identification card and/or vehicle/vessel registration information by:

Visiting your local DMV office (make an Appointment(s) for faster service)
Completing a Request for Driver Record Information form INF 1125
Showing identification
Paying the fee
If going into a local field office is not convenient for you or you are out of state, you may request your record by mail. Complete the INF 1125 form available on this web site or prepare a written request, including your name, date of birth, social security number, California driver license number, and your signature, along with a check or money order for $5, and mail to:

Department of Motor Vehicles
Office of Information Services
Public Operations Unit G199
P. O. BOX 944247
Sacramento, California 94244-2470

Court records, including the issuance of warrants, are open to the public and can be checked by any member of the public, though you will have to provide ID at time you conduct the search. A clerk can call the Sheriff and have you arrested while your there.

At this stage, it makes more sense to hire someone to find out if there are any warrants and then you can make a planned trip to deal with them, if need be. Your lawyer may be able to get the warrants recalled without an appearance.