My sister filed petition for me last year maybe I-130. I am an Indian and my wife is Italian, I am in California nowadays since last week. Can we stay here permanently under I-485 or AOS whatever?
That category takes 13-14 years. During the time you are waiting for your priority date to be current, you cannot stay in the USA just because your green card is pending. You can, however, stay or come to the USA under a visa independent of the green card such as L-1, H-1. You can also apply for a green card in several categories simultaneously.