It's just a colloquialism. It isn't possible for mythical deities to get offended, and "god" isn't a name anyway. The Judeo-Christian deity (which I assume you are speaking of) has a name, and it's not "god".
No it is not, many stated above that it is "taking the lords name in vain" but that is not true, the Christian God is not named "God" God is only a title, if you said his actual name as a swear word, then I would say it would be. But then again I do not know how a mythical being would be offended anyway.
The word vain essentially means empty, or void of any real value. To take God's name in vain is to evoke it in a hollow or meaningless way, without real significance or purpose to Him. In short, it is essentially to treat the word "God" in a valueless way. So it really doesn't take a rocket scientist to know that "Oh My God," used in this frivolous way, isn't really a call for God the father, it is simply used by habit or as an purposeless call upon God. Certainly it isn't an act of Christians agreeing with, evoking, praising or petitioning God. The truth is, this phrase is almost always little more than a bad cultural or social habit. It is unquestionably taking the name of the Lord in vain, which is a clear violation of His third commandment.