Virgil Stagg is an agent with American Intelligence.
In one of the scant three recorded adventures, it is stated by a character that Stagg was of "The U.S. Secret Service". However, that person was impersonating a British chauffeur and the "Secret Service" could have been just another way of saying Intelligence rather than referring specifically to the Treasury department. Also the type of missions that Stagg is shown to perform would not have fallen under the pervue of that bureau.
Whomever he works for, he definitely does not work for it alone because Virgil Stagg is but one half of a duo - the known half. The unknown partner is Leo Stagg, Virgil's identical twin brother who apparently has chosen to risk his life every bit as much as his more public sibling but without any recognition except behind the scenes. It could be that even the Staggs' boss at Headquarters does not know that Virgil Stagg is not working by himself though that is conjecture and would seem hard to believe.
The Staggs are likely in their late twenties or early 30. Short dark hair, good lucks, and fairly good athleticism are the more obvious traits discerned from the illustrations. Based on their actions, they are both quite fearless. Based on the results of their actions, they are both prone to getting physically abused and are incredibly lucky to both still be alive. In the three missions we know about, one or the other is shot, beaten unconscious and thrown from a high trestle into the sea to drown, and shot again while leaping off a balcony onto the stair below.
By the mishaps that befall them, it might be thought that they are less than qualified for their dangerous work but the fact that they have obviously had a good number of missions before and the fact that despite the injuries they both survived does show that they are resilient.