If they've used a "freebie" account such as Hotmail or Yahoo there's probably very little you can do. Microsoft or Yahoo should log IP addresses and logins somewhere, but actually contacting them and speaking to somebody who can trace this information would be tricky - and they've probably used an anonymous portal (i.e. Internet cafe) anyway so tracing that would be next to useless.
As this is a case of fraud, surely your credit card provider, together with the appropriate law enforcement agency, should be persuing and investigating this on your behalf?
Also; the email address they've used is probably a fake anyway - the email order confirmation could have been bounced back, which could be the reason they've contacted you by 'phone.
You could, at best, attempt sending an email to
abuse@whatever_domain_the_email_address_uses.com and give them the appropriate information.
Good luck.
Cheers
ZB