If I work at home in NJ but all my tax was withheld in NY do I have to pay NJ and if I don't is there any way they could prove I didn't work out of NY (my w2 is from NY), and is it worth to do this or NJ has a cheaper tax rate and if I file for NJ will I get a penalty and how much will it be

If you worked EXCLUSIVELY in NJ, but your employer wthheld NY taxes, the first you should do is to get your employer to change the withholding to NJ for 2008. He is required by law to do this.

Now, you must file BOTH a NJ and a NY tax return. Since you never worked in NY state proper, you will file as a non-resident and claim ZERO NY income, resulting in your receiving ALL of your withheld NY state income taxes back (NYC too if your employer withheld those taxes as well). Attaching a memo from your employer stating that you NEVER worked in NY to your NY state return would be advisable.

Now, you have to file a NJ state return as well. Attach a memo from your employer stating that they inadvertently failed to withhold NY taxes from your pay. The credit for taxes paid to NY does not apply here because you are getting a 100% refund.

You should ask that NJ waive any under-withholding penalties when you send in the check. All they can do is say NO, and there is a real chance that they will waive the penalty if you state in your own memo that you have arranged to have NJ taxes withheld from your pay.

Under-withholding penalties vary from state to state. My educated guess would be 1% of the tax due, but that is only a guess.