Assuming you were never domiciled in VA during the tax year and you were a W2 employee, you would file VA Form 763S to obtain a refund of taxes erroneously withheld by VA. See page 6 of https://www.tax.virginia.gov/sites/default/files/2017-01/763-2016-instructions.pdf
As a PA resident, all income is reportable on a PA income tax return, regardless of where earned. So this income needs to be reported on the PA resident income tax return and taxes paid. You will also need to file a PA local earned income tax return with the municipality where you live.
Edit to add: PA has a reciprocal agreement whereby a resident of PA will only pay income taxes to PA if they perform W2 work in VA, MD, WV, NJ, or OH.
Here are a couple of detailed articles on taxes for travel nurses, specifically "tax home"
<a rel="nofollow" target="_blank" href="http://healthcaretraveler.modernmedicine.com/healthcare-traveler/news/modernmedicine/modern-medicine-news/what-does-tax-home-mean-travel-nurses?page=full">http://healthcaretraveler.modernmedicine.com/healthcare-traveler/news/modernmedicine/modern-medicine-news/what-does-tax-home-mean-travel-nurses?page=full</a> and <a rel="nofollow" target="_blank" href="http://www.thegypsynurse.com/tax-home/">http://www.thegypsynurse.com/tax-home/</a>
Assuming you were never domiciled in VA during the tax year and you were a W2 employee, you would file VA Form 763S to obtain a refund of taxes erroneously withheld by VA. See page 6 of https://www.tax.virginia.gov/sites/default/files/2017-01/763-2016-instructions.pdf
As a PA resident, all income is reportable on a PA income tax return, regardless of where earned. So this income needs to be reported on the PA resident income tax return and taxes paid. You will also need to file a PA local earned income tax return with the municipality where you live.
Edit to add: PA has a reciprocal agreement whereby a resident of PA will only pay income taxes to PA if they perform W2 work in VA, MD, WV, NJ, or OH.