Oh started out his professional career with Suwon Samsung Bluewings in 2010. He made just 5 league appearances before being loaned to Gangwon FC for the majority of the 2011 season. He played 22 matches and scored once as his side finished 16th and last in the final standings, however they retained their league status due to their being no relegation from the K-League that year. He signed for Gangwon permanently in 2012 and made 31 league appearances to help them to a 14th-place finish, just above the relegation spots. In 2013 he joined, then J2 League side, Gamba Osaka who had been relegated from J1 League the previous season. His first year in Japan was spent largely as a reserve behind veteran right-back Akira Kaji and he made just 5 appearances as Gamba bounced back at the first time of asking, ending the season as J2 League champions. 2014 got even better for the men in blue and black as their return to J1 League saw them go on to win the domestic treble, lifting the J1 League title, the J.League Cup and the Emperor's Cup. Kaji departed for America before the season and Oh saw himself in competition with the newly acquired Koki Yonekura for the right-back position and Hiroki Fujiharu for the left-back slot. Due to a gruelling schedule, all 3 were rotated by coach Kenta Hasegawa throughout the year and Oh ended up making 37 appearances in all competitions. Gamba retained their Emperor's Cup title in 2015 and added the Japanese Super Cup to their trophy cabinet, they also reached the semi-finals of the 2015 AFC Champions League before going down to Chinese outfit Guangzhou Evergrande over 2 legs. Oh didn't feature nearly as much as he had the previous year as Yonekura and Fujiharu locked down the starting berths, he played just 10 times in the league and 22 games in total. He was also red-carded in the league championship final play-off first leg at home to Sanfrecce Hiroshima. With Gamba leading 2-1 in the 86th minute, Oh was shown a straight red-card. They went on to concede injury time goals to Sho Sasaki and Yoshifumi Kashiwa and lost 3-2 before drawing the return leg 1-1 which led to a 4-3 aggregate defeat and Sanfrecce being crowned J League Champions. There were to be no trophies for Gamba between 2016 and 2018, but Oh went on to feature regularly for them in that period despite fierce competition not only from Yonekura and Fujiharu but also from the up-and-coming Ryo Hatsuse. Oh played 18, 29 and 24 league games respectively across the 2016, 2017 and 2018 seasons as Gamba finished in 4th, 10th and 9th positions.
