Tennessee and New Hampshire do not have personal income tax so no return would be required.
You would have to file a Virginia tax return if your Virginia adjusted gross income is equal to or greater than $10,950 single or $23,900 married or you were in the state or maintained an abode in Virginia for more than 183 days.
Anyone who is not a resident of Maine, but performs personal services in Maine for more than 12 days and earns more than $3,000 of income from all Maine sources, must file a Maine return. Up to 24 days performing certain personal services, such as training and site inspections, are not counted against the 12-day threshold.