(1) No, you will not get a criminal record. It is not a crime to fail to pay back a loan. Unless you committed fraud, loans are a civil matter. They are just lying to you to coerce you into doing what they want.
(2) If you do owe the loan and they have to go to court to collect it, then they usually are entitled to charging you for their legal expenses (attorney fees and court costs) which can be a lot.
(3) If you do owe the loan, they can hurt your credit rating by reporting the unpaid loan to the credit bureaus.
If you pay back any of the money, then you may be admitting that you owe the loan. So you should be careful what you say to them except to deny the loan and tell them you will report them under the FCRA. If you want to fight them, you need to research your rights and get legal advice.
However, if you did not sign anything, you may not have to pay back the loan. And they may have to stop bothering your per the Fair Credit Reporting Act (FCRA law). They can be liable to your for damages and they are committing a crime by lying to you about giving you a criminal record.