Perhaps the BEST B1G Forum anywhere, here at College Football Fan Site, CFB51!!!

The WWII teams were "weird" for several reasons beyond the Army thing.
First off, they were like college football all-star teams, fielding players who excelled at schools all across the country.
Secondly, they were allowed to have young pro players as well.
Third, those great players were on and off the roster, as they might be deployed at any time.
For example, Iowa Pre-Flight's depth chart and roster as a whole looked very different from one game to the next.

This is how weird it was for the Buckeyes:
Short version:

• 6-1-1 in 1941, finished #13.  
• 9-1 in 1942, won first NC.  
• 3-6 in 1943, finished unranked.  
• 9-0 in 1944, finished #2.  Interestingly Ohio State was the only non-Military team in the top-6:  1 Army, 2 tOSU, 3 Randolph Field, 4 Navy, 5 Bainbridge Naval, Iowa Pre-Flight.  

Longer version:
Ohio State hired Paul Brown before the 1941 season.  I've said before that I think Paul Brown was the best coach to ever coach in the BigTen.  He can't be considered the best coach in BigTen history because he was only in the BigTen for three seasons (1941-1943).  

Paul Brown was a phenomenal coach as evidenced by all the success that he had at the professional level.  In his first year at Ohio State (1941) the Buckeyes went 6-1-1.  The tie was at Michigan (finished #5) and the loss was to Northwestern (finished #11).  The tie with Michigan was a huge upset considering that the Wolverines were #5 and the Buckeyes were #14 coming into that game.  

Brown's second season was 1942 and he won the NC.  The only loss that year was to Wisconsin.  My understanding is that the Buckeyes travelled to Madison on train cars that had been out of use due to the war and most of the team got sick from drinking stagnant water in those disused train cars.  It might be easy to look at this and diminish this accomplishment because it IS Ohio State and they have been a helmet for so long that winning NC's is "what they do" but this was Ohio State's first.  In fact, when Ohio State was ranked #1 in the initial poll of 1942, it was Ohio State's first ever #1 ranking.  Paul Brown really established Ohio State as the "Helmet" that they are today.  

The 1942 season was played mostly with guys who had been on the 1941 team and hadn't enlisted yet but at the end of the 1942 season basically the entire team joined the military.  As mentioned upthread, schools such as Michigan and Purdue were part of the Navy's V12 training program which allowed trainees to participate in varsity sports.  Ohio State was part of the Army's "Army Specialized Training Program" which did NOT allow trainees to participate in varsity sports so the 1943 Ohio State team consisted almost entirely of 17 year old true freshman not yet old enough to enlist.  Unsurprisingly, they sucked.  They lost to Iowa Pre-Flight, GL Navy, Purdue, Northwestern, Indiana, and Michigan and only beat Mizzou, Pitt, and Illinois whom I believe were in the same boat vis-a-vis military training.  

Paul Brown joined the Military after the 1943 season and ended up coaching GL Navy in 1944.  One of his players there was a halfback named Ara Parseghian.  After the War the Ohio State Athletic Department assumed that Brown would return and build on what he had already achieved in 1941 and 1942 but alas Professional Ball came calling and Brown became the first coach of the Cleveland Browns where he won 4 AAFC Championships, 3 NFL Championships and numerous COTY awards.