Things like this are really hard - from OMG to butt/tush/yukky there are a bazillion things other families won't like and it is nigh on impossible to anticipate all of them or to expect little ones to remember what-to-say-in-who's-house.
Personally, I wouldn't worry about it if it was someone in the park -- even if they said something to me, quite frankly. However, if it was my friend, whom I care about & hang with a lot and whom my kids hang with a lot, I would absolutely hope that he/she would tell me if there was a phrase I was using or my kids were using that upset him/her. Friends are part of our family.
I'm not any particular religion, but OMG would bug me, too. Not enough for me to say something to someone else probably, but enough to let my child know it's not an OK thing to say. I don't really even know why I feel that way-- I guess because I don't like hearing children use expressions/words that they don't fully understand, or don't understand the impact of.
As for the taking the Lord's name in vain, I don't know... I've never thought that was quite what the Lord meant. I mean, how then do you define what is "frivolous" and what isn't? I hear people tossing out "praise the Lord" constantly when it doesn't seem particularly connected... kind of like a stock response. Is that in vain, or is it not considered vain simply because it has a positive connotation? If you tell a friend something and they are shocked and truly stunned and say "OMG" it can very well NOT be in vain, but be truly heartfelt and a way of expressing shock and sorrow that only God can help them understand. My interpretation of using the Lord's name in vain, is to make frivolous promises and swear against His name when you don't really mean it. I find "swear to God!" much more offensive than OMG. Especially since it's usually used about the truth of some ridiculous thing that is not worthy of such a swearing! KWIM? Don't mean to derail the thread onto a discusion of that, though. Oops.
Basically - it's your friend and it seems like you know she cares about you & would never knowingly offend. You don't have to make her feel guilty or anything, but the longer you let it go on the more she has to feel guilty about! So I say to say something and just be matter-of-fact and loving about it - don't over-apologize for saying something (a sure fire way to instill guilt.) I'll be willing to bet that if there was something you were saying offhandedly that upset her, you would want her to tell you, right? Of course right!