Your options are to use it as a rental, short sale or foreclose.
If you have a hardship such as a forced relocation to find work, this will help with a short.
You need to get educated on your loan(s) and the implications if you walk. Were they purchase money or refi money? Is there a senior and a junior lien? In Nevada, are there judicial foreclosures? Is there recourse on the lien?
I strongly urge you to find a successful real estate broker who has a proven track record of closing shorts and can give you counsel. You also need to speak with an accountant as well as a lawyer. These are big, life changing decisions and this is not the time to try and go commando.
The only way to sell your house is to short sell it. You don't neccessarily have to be behind on your payments to do so, depending on the bank your mortgage is with, but you have to be able to justify to the bank why they should take less money than is owed to qualify for a short sale. You will need to discuss your situation wtih a default resolution specialist to see if you can qualify for a short sale in your particular situation. I can't tell you if you might without doing full financials so please feel free to give me a call for a consulation if you would like to pursue this possible option.
Nice idea to trade it, but who would want to take on that excess debt? I'd say it would be very difficult to find a willing "trader" for that- and the bank would call the loan in full most likely- check out your deed of trust and see if it has a due on sale clause. Almost eveyr mortgage does, and when the new owner goes to put the title into their name, that would trigger the clause, so basically they would now owe ALL the money on the note at once.