The Italian agency will have nothing to do with your taxes if you are only liable to pay tax in the US. All they need is your bank details to wire you the money. You need to take care of state and federal income tax yourself.
(I am a US translator working for European companies.)
I have a question about invoices. I have just finished a translation for an Italian agency and now I have to send them my invoice. I live and pay taxes in the US, although I am an Italian citizen. What kind of tax information should I include on the invoice? They shouldn't need my SSN, should they? And at the same time, as an Italian citizen resident in the US, I know that I don't have to pay taxes in Italy, so I don't think I should include my Italian tax number....if all this is correct, then what shall I write on the invoice?