OSU is accessible as a guest of a member, alum, faculty or student. The other way to play is to join the Buckeye Club and then join the golf course. Finally, the course hosts lots of events, so getting a chance to play is not difficult.
I used to play OSU all the time as a student. Unfortunately, Scarlet was renovated during my third year of law school, when I was hoping to play an insane amount of golf. I've played it probably 5-7 times since the renovation. It's definitely more of a tournament course than a members' course, but still an enjoyable course to play (if you're on your game). Much of the original MacKenzie is gone. It's now more of a Nicklaus-type course, but not in the same vein as a "typical" Nicklaus course. Gray is very much a "fun" course and definitely worth playing. I think there was some discussion recently about someone doing a renovation of Gray, which would be spectacular. It might have been Dr. Hurdzan, but I can't say that for certain.