Most unusual/mesmerizing female voice.

Jsaah, Totally agree thanks for adding her

Jane Relf . . . not necessarily that unusual (ie odd), but unusually beautiful and indeed mesmerizing.

Blossom Dearie

Lani Hall

Yoko Ono.

Dinah Washington, maybe not mesmerizing but definitely demanding of attention

Yma Sumac

I like Beth Gibbons from Portishead, she captivates me with her voice.

I first thought of Joanna Newsome because she is unusual but her voice does not mesmerize, me it annoys me...

Cat Powers is a good pick too.

Kudos for the Joanna Newsom pick. I throw Cat Power into the mix.

Joanna Newsom
Janis Joplin
Billie Holiday
Bjork

What about Barbara Streisand? Her new Village Vanguard release will keep your attention, or mesmerizing.

Jesse Sykes of Jesse Sykes and the Sweet Hereafter. Unusual AND Mesmerizing.

Laurie Anderson

Hope Waits

Holly Cole

#1 for me: Dusty Springfield
#2 Annie Lennox

agree, Margo . . .

Also, Hope Sandoval is up there

Oh Margo, sweet Margo...

Margo Timmins of the Cowboy Junkies .

billie holiday

Bjork ... and she IS unusual too!

Well, this may be a stretch but Antony Hegarty from Antony and the Johnsons comes to mind. I would argue that it is a female voice though not necessarily from a female. Joanne Newsome fits the unusual but some may feel not so mesmerizing. One I think would have more universal appeal is Marisa Nadler. I would strongly recommend giving her music a try.

Sia Furler, Joan Armatrading.

Yoko Ono has a very unusual voice but John Lennon seemed to be the only person that was mesmerized by it!!