Is filing an answer my only option when I'm sued in California?

No, and picking the wrong response option can genuinely waste both your money and your legal position. A demurrer is a specific procedural motion attacking a complaint on the grounds that it fails to properly state a valid legal claim in the first place. A motion to quash separately challenges defective service of the lawsuit or a lack of personal jurisdiction over you specifically. A motion to strike targets and removes improper material from within the complaint itself.

Each of these alternative responses shares the same 30-day deadline as a standard answer would. It's worth having someone assess which option actually fits your specific situation before you file anything, because filing a standard answer generally waives your ability to raise some of these other, more targeted procedural arguments later in the case.