Wilson racked up 132 yards and a score on 26 carries. Oglesby added 75 more and a pair of TDs on 12 attempts.
The Hokies (4-0) benefited from a 22-of-33 passing performance from Logan Thomas, who amassed 229 yards through the air and added a rushing score.
Virginia Tech -- which won a fourth straight to start the season for the first time since 2006 -- got a combined 173 receiving yards on 15 catches from Danny Coale and D.J. Coles.
Marshall (1-3) could manage only six yards rushing on 24 total carries in the defeat.
Rakeem Cato completed 17-of-33 pass attempts for 245 yards and a score for the Thundering Herd.