As far as the short sale you will want to get some things in writing immediately, if you do move out, your short sale may be dead before arrival. You need to talk to your agent and teh person negotiating the short sale for some answers, 3 years is extremely abnormal
please see my blog for advice and tiups on short sales
I believe that they are still entitled to rent until you own it. They could evict you for non-payment of the rent. I had an escrow recently with the buyer being a tenant and the owner collected rent and didn't pay the mortgage. My recomendation is that you pay the rent until you own it as long as the owner still owns it and not the bank. For the last month of the escrow once you are sure it's going to close you might discuss with your agent paying a partial payment of rent (pro-rated for the days you are going to own vs rent). Also, is your deposit being given by the seller to you in escrow? You might want to address this if the seller has lost or spent your deposit. This should be transferred in escrow and if the seller doesn't have it then perhaps your money you are paying for rent could go back to you. It's hard to give advice not knowing the specifics so please bring these questions/concerns up with your agent.
The Carrabba Group
Keller Williams Hollywood Hills
If you are being represented by a Realtor, you could go to them for some assistance, depending on what the answers are to some of these questions. It sounds like you need legal advice. Realtors who are members of California Association of Realtors have access to a hotline to help with understanding rights under the law and contracts. They wont represent you but the information they provide can be helpful. Good luck and post again with updates.
You can plead your case in landlord tenant court - and let the judge make the determination as to what you must do. You may consider (Upon legal consul advice) to hold your rent due in escrow until a judge determines the best practice.
Let us know what the judge says!