http://www.dmv.virginia.gov/webdoc/citizen/drivers/manual.asp
According to this publication, the driver who arrives FIRST at a 4-way stop has the right-of-way regardless of what kind of turn (if any) they are making. If drivers arrive at the same time to a 4-way stop then the driver on the left must yield to the driver on the right.
For example, if you're looking at the intersection from above and a car arrives from the west at the same time a car arrives from the north then the car from the west gets the right-of-way. East yields to north, south yields to east and west yields to south.
In NOVA, I try and avoid "arriving at the same time" to a 4-way stop. I do this by observing the other traffic as I approach, if possible. If I see what looks like someone could arrive at the same time I do, I trail my brake early so that they arrive first and can go first. Also, make lots of eye contact with the other driver and wave them through if in fact it's their right-of-way and for God sakes do NOT let your passengers get involved with waving people through whether your passengers are correct or not.
The reason I trail brake into the 4-way stop is because if you try and go and have an accident and there's no witnesses what's to stop the other guy from saying to the officer, "Nope...I arrived first to the 4-way stop. It was his fault." Obviously, they can interpret somethings based on the angle of the accident assuming the vehicles weren't moved, but why leave it up to that?