Lucinda Williams seems to be getting more so as the years go on.
Kristian Matsson (performs under the moniker "The Tallest Man On Earth.)
He’s Swedish but appears to mostly sing in english.
Wow. No mention of Rod Stewart yet.
The late, sorely missed Leonard Cohen.
John McCrea from Cake. At first listen, it sounds like he’s just talking over music, but there’s more to it.
Blossom Dearie, died at 84 but probably still sounded like she was 7 years old.
Honorable mention: IBM 7094.
Or maybe Shirley Manson, for a (far) less bizarre definition of “unusual.”
I always thought Judy Garlands voice was strange. And Joe Walsh does that weird blowing-into-a-tube guitar thing.
She mumbles, and it sounds like her tongue is swollen.
And the answer is: Doc Dart of the Crucifucks.
What do I win? 
…and Licorice McKechnie, who could shatter crystal and summon wildlife!
Eartha Kitt.
lemmy (rip) of motorhead … when I first heard him I said something to the effect of " dude sounds like he cleans out the homegrown pot residue in his throat with night train"
Su Tissue of Suburban Lawns.
I assume you mean now rather than then.
Brenda Lee
Cyndi Lauper
Nancy Griffith - who I love, by the way - but she has a voice kind of like a nine year old girl.
Ian Anderson of Jethro Tull and his use of melisma. I didn’t even know there was a word for what he was doing until I researched it. He was just the dude who could sing more than one note at the same time. His voice is shot now, but back in the day, it was certainly unique.
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Melisma isn’t singing more than one note at the same time. It’s when a syllable in a lyric has multiple notes sung in sequence to them (think of the vocal embellishments in Whitney Houston’s version of “I Will Always Love You.”) The only thing I could think of singing-wise that produces multiple notes at the same time is overtone singing, which is pretty odd and cool.
You sound like one of the unfortunates who heard his solo album. I’m another one.
One of the greatest practitioners of which was mentioned in Post #9.
Ah well, ignorance fought, then. Still, an unusual voice and I’m not completely convinced he didn’t employ overtones. A friend of mine once said that he “sang in chords.” Of course, he also would sing while playing the flute so that could have been part of it.