Unless you gave the store permission to access your information then it shouldn't have been provided by Experian.
However, there is no specific law that was violated since none of that information is protected. I can't imagine how Experian would know what kind of car you drive since they don't access DMV records, etc. They only have information that is provided to them by merchants.
Your birthdate isn't hard to find using a variety of online resources however they shouldn't have provided your SSN without an authorization. My "educated guess" is that if Experian did provide anything then the merchant told them you had allowed them to access the information.
If you had applied for credit, of rinstance, with the store then they would have had access to any information Experian had in their database. That would include SSN and birthdate.
Experian does have a verification service. You can see the basics of it at http://www.experian.com/decision-analytics/identity-and-fraud/identity-verification-screening.html
This info and service isn't regulated to any extent. Depending on exactly how the exchange of information took place it is possible some law was violated but there is no way to know from the information you provided so far.
What you may want to do is file a complaint with your state's Attorney General and see what their investigation reveals. That will tell you whether you want to pursue it further.