I work out of my home in Virginia but my company is based in NJ. Where do I pay state taxes.

You pay taxes in VA, because that is where you live and work. You owe no taxes at all to NJ.

However, you MAY have to inform your company of these facts of life in the tax arena. I have a number of clients who literally have to force their payroll departments to call the state tax office to confirm that they do NOT have to pay taxes in the state where the company is located, but NOT where they live and work.