The way I understand it, Japanese doesn't have "swear words" the way we think of them. There are very disrespectful ways to refer to people, but they're not treated like evil incantations the way they are in English -- everyone knows what the words are, and everyone knows not to use them. TV shows that would be the equivalent of TV-Y7 over here often have characters using those words, which are translated as "*******" and the like in faithful dubs, because those fictional characters are in situations where they have reason to be that angry at other people, and the kids watching are expected to understand that just because the people on TV say those things doesn't mean they should say them to people in real life, just like you shouldn't kill people in real life.
When you think about it, it's funny that kids' shows in America can have killing, but not swearing. Think through the logic on it. Why are swear words bad? Not because of any inherent power in the words themselves, but because of the feelings of anger and hate and disrespect that they are carrying. And ultimately, anger and hate and disrespect for others is bad because it eventually leads to killing them. It'd be like if it was okay to show people having sex, but not show them flirting (On the other hand, maybe it's like how it's okay to show people who have children without showing the sex they had to make the children?).
I think we focus too much on the taboo of the specific words. We call them "curse words" as though the words are magic. They're not. That's silly. And the whole argument for not letting kids know what the words are is "But once they know them, they'll start saying them!" which is probably only because we try so hard to keep them from saying them.
As to the religious aspect: The verse that Christians most often use to prohibit swearing is "Do not take the name of the Lord in vain." That would only cover things like "oh my God," "god[darn]," and "Jesus H. Christ" (and, if you look into the etymology, "egads" ("Oh gods") and "gadzooks" ("God's hooks," referring to the nails that held Jesus to the cross)) (also some Christians say that "jeez," "gee," "gosh," "golly," and the like also count, because you're really still saying the same thing). There's another verse or two somewhere in one of Paul's epistles about not having "coarse speech" that is sometimes also used when it's pointed out that most words we consider swears don't have anything to do with God's name.
However, in the original context of the "taking the Lord's name in vain" thing, it wouldn't have been referring to saying "oh my God" anyway. It would have referred to someone saying that God said something that he really didn't -- taking something that's really your own opinion and/or for your own gain and attaching the name of God to it to give it legitimacy. Westboro Baptist Church is an excellent example of people actually taking God's name in vain. Virtually all televangelists, too. And a lot of politicians.