I didn't file tax for 2009 and 2010. I'd like to file it now.

My situation:
I'm an international student with F-1 visa since 2008.
In 2009 and 2010, I lived and worked in NJ. I received W2 for both 09' and 10'.
In 2011 I transferred to a school in NY and since then I've lived in NY.

My questions:
For state tax for 2009 and 2010, I need to use Form NJ-1040, right?
For home address (both federal and state), should I put my old address in NJ or my current address in NY? (I no longer live in NJ)

Thanks.

Use your current address, so you can receive their mail to the proper address.

And file Form NJ-1040NR.