A couple months ago my landlord informed me that the house I am renting was going into short sale. His agent told me I would have priority over the other offers because we were renting. I was waiting for a response from our offer and have just found out another offer was accepted. How much time can I have to continue to look for another home when we do not have a lease? I live in california.

Checking into the landlord tenant laws in California should be your next step.  That way you will know all of your rights as a tenant.  Your best course of action would be to start looking for another another property to purchase or rent immediately.

It could be possible that they may have overlooked your offer and thought you never presented anything to them. Why not check in with them again? If they were sure about taking someone else's offer, then you can use the opportunity to clarify how long you have to move out. Verify their response with whatever California law says.