My understanding was that while they all have the same hiragana "spelling" (still don't like that word)reading, they are in fact completely different words. Which the 3 definitions that you have mentioned Dave being in line with how I would use and have seen these kanji being used in Japan.
So to answer your question, i think the Edict is incorrect. Looking at some of the other comments it seems that they are listed properly, at least from my perspective, as separate entries in their dictionaries.