Ohio State has some history with the service academies at the highest level of college football. The Buckeyes have played against Navy five times now (winning every time), mostly recently to open this year, a 34-17 victory for the Buckeyes. Air Force can claim an undefeated record against Ohio State, and is the last team to beat Ohio State outside of the Power Five, a 23-11 loss in 1990. Ohio State has never faced Army.
That could potentially change, however. According to the beat writer covering Army football, the two schools are in talks for a possible football game after the 2016 season. Ohio State is completely booked for the 2015 and 2016 seasons.
Unless currently scheduled games are moved, the soonest the two squads could face each other would be the 2017 season, where Ohio State is also scheduled to host Oklahoma and UNLV. The Buckeyes also have an opening in 2018 (Oregon State, at TCU), and 2019 (TCU, Cincinnati).
It's most likely that any agreement with Army would be a single game event in Columbus, but the Buckeyes did play a second game with Navy in Baltimore, so a return trip at say, Yankee Stadium or MetLife Stadium wouldn't be out of the question.
Any agreement with Army is not likely to boost any strength of schedule for Ohio State. The Black Knights have only made one bowl game since 1997, a 2010 Armed Forces Bowl appearance after a 7-6 campaign. Army went 4-8 last year.
(H/T: College Football Talk)