Hey there, Sergio. To answer your question, I would attempt a short sale. Depending on your situation and the type of loan you have, more than likely you will not have a deficiency. I can give you a better answer after I get more information from you.
I wouldn't recommend renting the house. How hard is it going to be to manage when you are out of state? What if the tenants stop paying? What if a pipe breaks and floods the house? I'm not saying don't rent the house. I just know from past experience that managing rental property from a distance is super tough. I knew a real estate investor who targeted what he called, "tired out-of-town landlords." He would offer to buy their property below market.
Surprisingly, many of them accepted his low-ball offers because they were so tired of dealing with the property. Here is the other downside on renting: you will probably have negative cash flow every month. I don't know what your house will rent for, but if you are upside down on your house value then you are likely also upside down on the rental value. That means you will almost certainly lose money on the rent every month. With your precarious financial situation, a recent 30 percent salary cut, and a move out of state,
the last thing you need is another bill each month.
With a short sale, you can walk away owing nothing and without tax liability while being eligible to buy another house in three years. That sounds a lot better to me than being stuck with a money losing house two years from now.