I'm a local history geek. One of the things I do is keep track of significant anniversaries in our local schools and draft commending resolutions for significant anniversaries.
Here's a list that I've compiled for the founding and closing dates for our area local schools. Woodlawn Elementary and Groveton Elementary are the oldest followed by Mt. Vernon High School. There's a great history of Woodlawn Elementary School here.
If you're talking about the actual buildings, I'm pretty sure that Woodlawn Elementary is the oldest in continuous use. The old Mount Vernon would be second if it were still a school. I'm pretty sure that either the Bryant Building (originally Groveton High School) or the older part of West Potomac High School (originally Bryant Intermediate) would be next.
I have some schools here on the bottom that have come and gone through the years including some from a very long time ago. The Gum Springs School and Springbank School were small black schools that preceded desegregation.
If you have any of the dates that I'm missing or any corrections, shoot me an email.