I live in NY (not NYC) and work part-time in NY for a company located in NYC. NJ State Income Tax and NJ SUI/SDI Tax are withheld from my paychecks, as well as NY State Income Tax and NY SUI/SDI. I have not worked in NJ and do not live in NJ ever.

How do I recover that $$ and what form does my company need to stop withdrawal of anything to NJ?

First - talk to your payroll department and make sure that they are no longer withholding any NJ taxes. Make sure they have your correct NY address on record. They may need you to resubmit a form IT-2104 (withholding for NYS), see: Withholding Tax Forms 2009/2010 - Current Period (http://www.tax.state.ny.us/forms/withholding_cur_forms.htm)

Second - you need to file a non-resident tax return with NJ (NJ-1040NR), to document that you had $0 NJ-based income, and to get a full refund of the income taxes withheld.

As for NJ SUI/SDI - I'm sorry, but I don't know how to have that refunded to you. Talk to your payroll department about it - it's their screw up, so they should help you set this right.