Hi,
Here is some of my status.
I was on F1 from 2007/04 to 2008/12.
Starting from 2009/03, I moved to NJ and started working in NY as OPT.
2009/10 my visa status changed to H1b.
I rented an apartment with someone else since 2009/05, both of us signed the lease.
My company withholds my NY state tax and Federal tax since I started.
Reading through the tax law (pub. 519) and various Q&As on the site, I think I need to file 1040NR for federal. And also, I think I need to file IT-203 for New York State.
But the question is, do I need to file NJ-1040 or NJ-1040NR for New Jersey? As far as my understanding, the domicile requirement refers to a permanent home, which in my case is in my home country. I don't own a house/apartment in New Jersey.

Any help/suggestion is appreciated!

If you are not married, file nonresident tax return for federal.
For NY you are nonresident and will report all the income earned while present in NY.
For NJ you are resident and report your income including NY income. Claim credit for taxes paid to NY.