In general a report under oath and a sworn statement are the same thing, but whether you need to have the document attested to by anyone, and if so whether that person must be a notary or some other official, depends on the exact details of the order (which I have not read) and importantly what court in Illinois entered the order. I assume it is likely a federal district court, but it matters a great deal if it is instead a state court. So that information is needed to answer the question.

They would want that information to investigate what damages they might be able to seek for infringement. Whether you must provide that information depends on the details of the lawsuit. If the lawsuit is not yet concluded and they are asking this information as part of discovery in the case then you must provide that information or be subject to possible sanctions. 

I suggest you ask the US lawyer you hired to represent you in this about what obligations you have. If you have not hired a US lawyer to assist you, I would strongly recommend you do hire one.