Noel is supposedly doing a solo album, but I speculate that his post Oasis music will be mostly acoustic. Right now, however, I don't think he's too worried about it. I think he's kicking back and enjoying his money.
I do know that he sold his house in Ibiza, citing that James Blunt lives in the same neighborhood, and that he "just couldn't stomach living there knowing that James Blunt was nearby making horrible music.
Regarding Beady Eye: the two tracks released so far are pretty darned cool, especially if you can let go of the Oasis connection.