Can my wife be awarded our home in a divorce in Virginia. It is a VA loan, she is not on the deed, mortgage, and insurance?

It is possible.  Depends on many many factors.  Very importantly, WHEN was the house purchased.  If after the marriage, it is marital.  You MAY be able to trace a part of it to separate funds used for down payment, and then to an extent it could be part marital part separate.  What also matters is how much equity is in the property to be divided.  Even if brought into the marriage, and even if kept titled separately, a home with a loan that is paid during the marriage creates a marital interest in the home, to the extent payments made during the marriage have added to current equity value. Also, courts often rule to "temporary" use of the house while divorce is pending, and this can be awarded even to the party not on the title who does not end up keeping the house in the end.