Most unusual/mesmerizing female voice.

Lisa Gerrard
K.Bush
Bjork
Diamanda Galas

I may add some italian female singers, like Alice and Elisa, but I guess they're not so well known in the USA

but the one that mesmerizes me most, though not so unusual:
Kate Pearson
her voice is not "uncommon" but she definitively touches something inside me, her voice's vibrations cause resonances in me
I've read she now has retired and manages a hotel somewhere in a lonely place in the mountains; well, when I come to USA, no NY or LA, no Vegas, no Yosemite or Monument Valley: I'll go in that lost place and ask her to sing... :-D

I like her voice but I mistook her name (see my post above): she's obviously Kate Pierson, not Pearson*.

as I'm here, I also add some other votes:
Sinead O'Connor
Mimi Parker (Low)
Margo Timmins.

*q: is the pronunciation very different or quite the same ? my English is bad and I often mistake in these cases