Consumer Protection Law
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You're the victim of a scam and you should send no more money. Facebook does not run any sweepstakes or lotteries. The scam is well known and has been reported and discussed on Facebook forums. You can also read a warning about this particular fraud from the Better Business Bureau here.
The fact is that you cannot ever win a contest that you didn't enter, and you didn't enter this one because it doesn't exist. This is just an attempt by a stranger to fleece you out of money. Further you never have to pay out of pocket to get money you have really won. When you're a real winner, that money is already yours, and all the real contest would do would be to deduct any transfer expenses from the money they already have and then give you the balance free and clear with no other strings attached.
There's a lot of fraud on Facebook, including people who will friend you and talk about how they themselves won a lot of money in a contest and who are setting you up for a scam. You can sue these folks or have them prosecuted, but in order to do that, you'd have to know who and where they really are, and that is a tall order. Facebook is not going to reveal private information except after a court order, and in any case, one can easily set up a Facebook profile using completely false information.
So this is really going to be a job for law enforcement, because the only way you'll get your money back is if the authorities can find the folks who cheated you and bring them to justice. You need to report the fraud to your police and to the FBI. For internet fraud, the FBI wants you to use their Internet Crime Complaint Center, online at IC3.gov.