you need to call each of the credit bureaus and have them put a fraud alert on your account - it is free. Also have them send you a copy of the credit reports so you can check for anything wrong with them.
you can have them put a fraud alert on your credit every 3 months I believe, that will stop a lot of potential fraud on your accounts. Best to call your bank or the company you have that debit card with, cancel it and have them send you a new card.
My mom's credit card got used - without the card. Turns out it was a company that was packaging her prescriptions, they had her card number on file and one of their employees used it online or for over the phone purchases... If they had an actual card, they were probably more sophisticated crooks with the magnetic tape creator, then just slap it on the back of another card, run it thru the card reader and there you go.
it's no fun going thru that stuff.