Virginia does require state inspections, but in the Tidewater/Hampton Roads area it does not sniff check. The inspectors do look for the imissions equipment that came on that make/model/yr vehicle, if not installed: no sticker. Additionally the bases require the state inspection sticker for your vehicle to have a base sticker, I know thats true for the in state regristrations, not sure if they push the issue if its an out of state regristration that state inspection is not required.
Personal property is only required for VA residents. Those in the military only have to show the LES statement which has your home state of residence on it. Those that are in the military and have VA as a home state on the LES have to pay ALL that personnel property tax. The state was, in the process of eleminating the personel property tax, it was reduced some but still lingers on. It was based on 3.75 % of blue book value, then reduced by some 45% (I can't remember how much exactly) due to being phased out by the last governer. Now the state is in so far in the RED all the "suites" in Richmond want to keep it going for ever.