'오바하다' means that you behave differently than usual, usually exaggerate your emotions out of excitement or as an attempt to hide your feeling (the usage really depends on the situation)
I got this vocabulary from Korean movie called 우아한 거짓말 (Thread of Lies). In this film, mom of a girl who passed away due to an unfortunate accident is trying to overcome the sadness and maybe to do that, the mom acts unusually cheerfully. In response to that, the sister of the girl says '오바 좀 하지마' to her mom.
I'm not quite sure where the '오바' in '오바 좀 하지마' comes from, but I can only guess that it's Konglish derived from the English word "Overreact".
Anyways, this vocabulary is used frequently among friends!
If you are an English native speaker, please let me know other English equivalents for this expression. (I'm trying to learn English too! :) In the subtitles of the Youtube Video, it was translated as 'Stop being so campy'.
Also, for other Korean vocab with this movie's trailer, please check out http://www.laughingbeans.com/learn/class/178. Although this movie didn't made it big, it's pretty well-made film.