Woodchicks is on the way on your route from Norfolk, VA to OBX. However their bbq isn't all that it is cut out to be and you will be severely disappointed. It is very bland and not really worth paying for it.
If you don't mind taking a 15-30min drive off of your route, I would suggest going to Smoke from Above or Whitners for bbq. Their BBQ is tasty, although you could probably make better at home. Whitners is off of I264 by a mall (Lynhaven Parkway) and Smoke From Above (off Princess Anne Road) you will have to drive through the city of Virginia Beach as there is no close highway exit to it.
If you want a great deli sandwich there is a deli called Route 58 Delicatessant which is fantastic (Off Virginia Beach BLVD). It is a NY Style deli and you are garunteed to not leave hungry. The sandwichs are expensive ~$15 but it will feed 2 people no problem.
If you want a good sit down restaurant that is on your route, there is a place called Baker's Crust that is between Norfolk International and the Bypass to get to the OBX. It is off Greenbriar Parkway South Exit (Chesapeake, VA) past the mall in a strip shop. They have good gourmet sandwichs, good salads, great desserts.
I live about 10mins from the airport and have lived in the area since 1988
You will love the drive down to Hatteras Island once you get past the main I64 interstate. It is a nice peaceful drive in the country, then you will come up to the OBX Bridge where you will be in full relaxation mode. Although the drive down to Hatteras Island is quite a haul from Norfolk since it is one of the southern most islands of the OBX.
