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Yes, you can stream Hulu Plus through the Wii.
As far as availability..... Depends on the show. I can get Grey's Anatomy the next day. Walking Dead is not until the current season ends and then they load the entire season at once.
Don't know about live sports on Hulu, but we have "the Internet Channel" on our Wii menu, so we can watch shows that way as well - as long as the network streams it.