Correct California has a 2 year SOL for breach of an oral contract:
Code of Civil Procedure:
339. Within two years: 1. An action upon a contract, obligation or
liability not founded upon an instrument of writing, except as
provided in Section 2725 of the Commercial Code or subdivision 2 of
Section 337 of this code; or an action
CCP 458 from http://leginfo.ca.gov/cgi-bin/displaycode?section=ccp&group=00001-01000&file=452-465 states:
458. In pleading the Statute of Limitations it is not necessary to
state the facts showing the defense, but it may be stated generally
that the cause of action
is barred by the provisions of Section ____
(giving the number of the section and subdivision thereof, if it is
so divided, relied upon) of THE CODE OF CIVIL PROCEDURE; and if such
allegation be controverted, the party pleading must establish, on the
trial, the facts showing that the cause of action is so barred.
You can plead the SOL in an answer but the quickest way to stop the case is to demur, if the complaint shows that it is time barred.
I hope this information is helpful.