Legal Question in Civil Litigation in California

No, because you didn't sign a rental agreement.

Theoretically, you could have an oral lease for a term less than a year. You are not clear on this, as you state you never signed any agreement. You do not point out whether you orally agreed to a fixed term less than a year, or any other arrangements.

If you have no agreement at all, including oral for a fixed term, then you are a month to month tenant. To move out, you must give the landlord the same amount of notice as there are days between rent payments. That means if you pay rent monthly, you must give the landlord writen notice at least 30 days before you move. You would only owe for the period up to expiration of your notice.