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I'm a writer, and I don't see anything in AP or Chicago style for ellipses with anything other than 3 dots. Wiki says 2 or 4 is more informal. I've never seen it or heard an explanation for it.

Grammar Girl says three only: http://www.quickanddirtytips.com/education/grammar/ellipses?page=2

But evidently the OED uses two to save space! http://www.grammarphobia.com/blog/2008/12/two-dots-or-three.html

When I was a minion for a scholarly journal we used the standard three, but you ended up with four dots if you had omitted material at the end of a sentence. The last dot is a period, not part of the ellipsis.

ETA: I wouldn't use two. If the OED is doing it as their own style quirk to save printing space that's one thing, but messing with well-understood punctuation seems to me to be asking for trouble.

I do copy-editing for a scholarly journal and I've never seen a two-dot ellipses. I commonly see a three-dot and four-dot ellipses.

I was an English major, and was teaching High school English until they switched my assignment this fall. Students are NOT taught to do anything other than a 3.