It is legal in VA and WV, but is almost universally against school policy.
That is partially true. In Virginia you can legally carry on a college or university campus, except for the University of Virginia.
You can not carry in the gun-free zones in and around elementary, middle or high schools. If you have a CHP you can carry on school property, but you must remain inside your vehicle. This allows CHP holders to pick-up and drop-off students without breaking the law while in the gun-free zone.
VT policy prohibits carry, but it is policy rather than law. If you are visiting the campus and caught carrying you would, at worst, face trespass charges rather than a firearm offense. Students, faculty and employees would be discharged or expelled if caught with a firearm, per VT policy.
My daughter goes to VT and I carry concealed when visiting there. She however can not as she won't risk being expelled.