Go straight to VISA to deal with it. The major credit card companies have strict anti-fraud policies, and THEY will deal with SONY, so that you don't have to.

I had a similar thing happen to me a few years ago, but it was the credit card company that called me direct and asked if I had just made four transactions on XBOX Live, costing about $300 altogether. I didn't even own an XBOX (or 360), so I told them it wasn't.

They handled the paperwork, and sent me out a statement I had to sign saying I hadn't made the purchases. Microsoft sent out a standard form letter denying responsibility (the Mastercard rep told me to expect this and how I needed to word my response to it). I wrote the letter, as instructed, denying fault, and BOOM: saga over.

It's also worth noting that while the whole process took about a month, Mastercard refunded me the day of the first phone call.

TL;DR: take all the info straight to your credit card company and they'll sort you out.

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