Virginia is a "right-to-work" state. I've never heard of the term "at will" state. What states are?
Really? The at-will doctrine is hardly new. I just googled "at will" and came up with thousands of matches. This one was the best: http://www.rbs2.com/atwill.htm which is a history of at-will employment laws in the United States.
All of them. Your employer can fire you for a good reason (you're drunk on the job), a bad reason (he doesn't like the fact that you wore a green shirt to work) or no reason at all (usually the best approach- just fire someone and don't give them any reason).
There are some limitiations, such as racial, gender etc, discrimination. However, gunowners are not a protected class. Your employer can legally fire you for exercising your 2nd Amendment rights.