Of course, words take on different (and sometimes surprising) meanings in different contexts, and I'm not a native speaker.
So anyway, I would not use EDICT as my sole source for "there is no word" or "the correct word is..." If I cared, I would probably read through the Japanese newspaper coverage until I found a word that seemed relevant in both dictionary definition and actual context. If there is no word for the phenomenon or it never happened, then you wouldn't be able to prove anything... but if there is a word and it did occur, then you would have something a little more solid than "I googled for Japanese dictionary and found some words in them."
It certainly is far better than any e-dictionary I could find for French back when I was forced (by law) to attend French class. It definitely helped a lot when I was in college (and, admittedly, situations where I used the wrong word)
For arguments sake: http://eow.alc.co.jp/%CE%AC%C3%A5/EUC-JP/ has lots of usage examples of 略奪 in context suggesting it does in fact mean looting.
The question left open, though, is whether that's the word reporters normally would use. It's not clear in the examples whether or not the word is being used hyperbolically. I mean, just because you can say "Muhammad Ali annihilated his opponent" doesn't mean that "annihilate" is a synonym for "defeat".
about the increase of looting in Japan following the earthquake uses 略奪 to refer both to armed robberies and taking things from unattended stores.