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

Joni Mitchell

Chan Marshall(cat power)
Natasha Khan(bat for lashes, SexWitch)
Sigur Ros(wink)

Mesmerizing:
Karen Carpenter
Lalah Hathaway
Doris Day

Unusual:
Nina Simone
Betty Carter

+1  Chante Moore

I realize i'll be showing my age (67), but the one I could listen to all day is Jo Stafford. Just something about her voice. Not everyone's cup of tea but maybe some of you geezers will remember her.,