Unfortunately NJ is one of the few states that taxes remote workers if the company you remotely work for is located in NJ.
Therefore, you will need to file both an NJ nonresident state income return (to report your NJ income while working remotely for an NJ based company) and a Part-year VA resident state income tax return to report all income from all sources (including NJ sourced income) while you were a part-year resident of VA.
You will not have to file in TX, because TX has no state income taxes.
You will want to work on your NJ nonresident state income tax return first. You will then take a tax credit from your NJ nonresident state income taxes on your VA part-year resident state income tax return. (Please note that you will only get a tax credit for your NJ nonresident state income taxes up to the amount of VA state income taxes that would have been paid if the income was earned in VA). The credit for taxes paid to another state section will be at the end of your residence state's interview process.
Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return
Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)