Okay, you just lost me there. None of that makes sense.
Iran does not yet have nuclear weapons, and even if they did, they'd have only a handful of fission weapons. They probably wouldn't use them immediately - Iraq is not a threat, and Israel is enough of a threat to not want to start a war with unless they have an advantage.
China will not nuke North Korea - that's like saying the US will nuke Canada. They'll probably also stay uninvolved at first, making a move on Taiwan and the Senkaku Islands (or whatever you want to call them, that's just the only name I remember) once the US is sufficiently occupied elsewhere. Japan might get nuked over the islands, but not likely.
North Korea is probably smart enough to hunker down and sit this war out as well. If they're dumb, they'll wait until the US moves troops out of South Korea before invading and promptly getting their asses kicked. They'll do some heavy damage, but they'd end up dead. China might then retaliate, but with the US out of Korea that's not a sure bet.
Israel will also do little - maybe take care of Syria, or if they get invaded they'll murder whoever tried, but they've got no horse in this race.
In your "everybody with nukes must use them" spree, you forgot Pakistan and India. I don't know how that one would turn out, but they don't seem to really want to conquer the other, just threaten them.
And in any case, even if every nuclear country except US and Russia got together, they still wouldn't match our arsenal. If you want a good metaphor, imagine nukes as guns. India and Pakistan are in a Mexican standoff with handguns. Israel has a PPK up its sleeves. China's eying everyone with an old SKS. North Korea's got a starting pistol they slapped a cheap round into that will probably hurt them more than whoever they shoot it at, and Iran has a kit of parts they haven't assembled yet. Meanwhile, America and Russia have .50-caliber machine guns ready to sweep the room. That's basically the worlds' nuclear powers right now.