I live in New Jersey. Can I file a small claims case online against a business HQED in Nashville, Tenn.?

It is doubtful since you would have to show that a NJ court has jurisdiction over the Tennessee corporation and they would have to be served in Tennessee. If they have a registered agent for service of process in NJ, then they can be served here in NJ. But if it is an online business you will have trouble if they are not registered for business in NJ. You may want to discuss with an attorney. Sometimes, writing to agencies like online BBB and filing a complaint can get some results without going to court.