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According to the official Mass Effect Twitter account:
Unfortunately it [Omega] will not be available for Wii U.
But not all is lost! In response to the question "Will there at least be any Mass Effect DLC (multiplayer or single) for Wii U? Besides what's on disc" they had the following to say:
Never say never. :)
According to the Wii U Mass Effect 3 Special Edition website, the From Ashes and Extended Cut single-player DLC will be included along with a new heavy weapon, plus the Resurgence, Rebellion, Earth multiplayer DLCs as well, so Wii U users won't be missing out on all that much. And with any luck, who knows? We might just see Omega on Wii U at some point.
'Sup world! I'm an avid gamer, modder and game developer living in Melbourne, Australia with my partner and two cats. As is law here at Player Attack, I can't function without copious amounts of caffeine.