One more option you may want to consider is refinancing your car and putting as much debt as you can on that.
However, keep in mind that you probably only want to do this if your car is in good running order and you feel that it will last until the end of the loan term. That way, you can take advantgage of the lowest interest rates, then just make your required payments on the vehicle loan and put as much money as possible towards your credit cards.
As far as unsecured loans go, it probably will be difficult to get one for that high of an amount, at least without going through a finance company (read extremely high interest rates) without a fairly high income and a low debt to income ratio.
If you decide to forgo the loan, concentrate on paying off your cards one at a time, starting with either the lowest balance or preferably the highest interest rates. Once that card is paid off, roll the payments on to the next card. You'll pay them off quicker than you thought you could
If you have any more questions, just ask