To Putin33's point about looking at a map. Here's one with the islands in dispute.
http://upload.wikimedia.org/wikipedia/en/c/cf/South_China_Sea.jpg
Here again is the Nine-dotted Line
http://www.bbc.co.uk/news/world-asia-pacific-13748349
See how much farther China's southwest claim goes than there are islands? How close the line is to Malaysia when the islands are farther off? The line goes well beyond where the islands actually are, and even extends to empty ocean way closer to Indonesia than any of the islands in question. These claimed waters do however, have oil and gas that would rightfully be in Vietnamese, Malaysian, or Bruneian EEZs. How convenient.
"Somebody explain to me how they can simultaneously control the islands as internal territory while it not being Chinese territorial waters."
Territorial waters extend 12 miles form shore. If the islands are rightfully Chinese (and they may be) then that's what they would get. If they're inhabitable they would also get an EEZ (exclusive economic zone) extending 200 miles from shore. Even if it had a 100% legit claim to all the islands and they were all deserving of an EEZ the Nine-dotted line would still have no basis in international law.
"All this complaining about 'freedom of the sea' when the whole point of controlling this area is to ensure that the US cannot cut off Chinese energy supplies via the Strait of Malacca, which it bullies its southeast Asian puppets into controlling."
Even if that were true, wouldn't absolute Chinese control of the sea mean it could cut off Japanese and South Korean energy supplies? And it isn't true, since ships can pass through the Strait of Malacca without Indonesia or Malaysia's permission due to the principle of innocent passage. Unlike China, neither of these states have been hassling ships moving through the strait in transit.
Perhaps in a war the US Navy would try and close the strait, but that would require the cooperation of at least one of the states by the strait. If this whole Malacca thing is even a real part of the Chinese calculus, they're asking to permanently control what is now a free international waterway because someday maybe America could close another international waterway during a war.
"It is US militarism which is threatening to undermine freedom of the seas, since this issue was a minor local dispute until America had to interject itself into it."
Asian states were actually moving away from the United States and looking for closer cooperation with China until China pressed the issue in recent years. After the Cold War the Philippines kicked us out of Subic Bay, now they expect us to join them in a war with China if it ever happened. The US military wrecked southern Vietnam for decades, but now the still communist government is looking to cooperate with America because a South China Lake is not in its interests. It is China's actions which are dragging the US back into Asia, not American militarism butting in.
"The US isn't even a signatory to UNCLOS, yet we need to hear Invictus prattle on about how Uncle Sam is defending the sea lanes."
We should sign on to the Law of the Sea. Because of this issue we probably will, and we only haven't yet because some parts about resource extraction are mind-numbingly stupid. However, the UNCLOS in large part just codifies what is ALREADY customary international law. That means it's already international law, and needs to be followed.
And interestingly, the PRC has already ratified the treaty, so it is unambiguously bound to follow its provisions. That's probably why it won't take the issue to any international tribunal. It can't win on the Nine-dotted Line claim so even if it gets all the islands it will look like a defeat. The CCP doesn't need a crisis like that.
China's so obviously in the wrong here. If you need to support a communist state here just pick Vietnam.