Alpha/beta/omega is one of the weirder fanfic tropes, and popular. I like it either because it's porn or because it's weird biology. Not sure which. I think it varies by the fic.
Jim Moriarty (BBC Sherlock)
Jim is an omega. That's not really the surprising part - omegas make up a significant though relatively invisible minority of the (alternate) world's population. The surprise is that he is overtly an omega in his public and personal life, though he keeps his identity relatively confidential. He neutralizes his natural scent not to hide, but to be enigmatic. He deals with alphas as his victims and minions, not as his superiors. He appears (appears) to lack an omega's natural submissive instincts.
Sherlock Holmes
Sherlock is a beta, the only gender wired to be asexual. Sherlock's dislike of hormonal idiots is pronounced, in this universe, into a sort of universal sexism and superiority.
Irene Adler
Female alpha, obviously. Also, rewriting her to be a lot closer to Victorian canon, because what the hell.
John Watson
While he could be a closeted and impressive omega, I'd put him as an impressively mild mannered alpha often mistaken for a beta.
Mycroft Holmes
An enigma.
Mrs. Hudson
Omega, and quite a wild thing in her youth.
Lestrade
Beta.
Molly Hooper
Beta.
None of which gives a plot to the story vaguely floating around in my head, but what can you do.