I have been here on many working visas , paid taxes in the US and thus registered to AIRE Italian Registry for Resident Abroad at the Italian Consulate. The registration is mandatory to people who stay for a period longer than 90 days, abroad.
I'm now on a G1 visa with an ordinary passport, paying taxes in Italy. What should I do with the AIRE? Should I still be registered? Am I considered fiscal resident in Italy and physically resident in the US?

To my knowledge, No registration is required, though that is REALLY a LEGAL question, NOT a tax question.

Tax-wise, due to your G-1 visa, you are TOTALLY exempt from ALL U.S. taxes, both federal and state, on your EARNED income.

If you make OTHER forms of income (like stock transactions), you MAY be liable for a tax return on any income from such transactions. I would have to research the U.S.-Italy Tax Treaty to be sure.