This is complicated due to the rules of the states. The easiest way is to file Married Filing Separately for both federal and state. However, there are big tax consequences to that: higher tax rate and many credits are not available.
According to both states, you can file federal Married Filing Jointly and then Married Filing separately for New Jersy and Virginia. To do that you must calculate income and exemptions as if a federal married, filing separate return had been filed.
New Jersey:
If you are married and file a joint federal return, you must also file a joint New Jersey return. If you file separate federal returns, you must also file separate State returns. If during the entire tax year one spouse was a resident and the other a nonresident, the resident can file a separate New Jersey return. The resident calculates income and exemptions as if a federal married, filing separate return had been filed. You have the option of filing a joint return, but in that case, your joint income would be taxed as if you both were residents.
Georgia:
If one spouse is a resident and the other is a nonresident without any Georgia-source income, your Georgia return may be filed jointly or separately with each spouse claiming the appropriate exemptions and deductions.
If you have more questions about this, ask in the comment below.
[Edited 03.25.19|11:22am PST]
