Bob Brozman's relatively recent album with the Tau Moe Family will give you a fair sense of what the vocals sounded like, as will some of the family's old recordings as Mme. Riviere's Hawaiian's--they began recording in 1929, but even then, their music was regarded as old style, which meant that it sounded more like the Hawaiian music from before the turn of the century--

The singing has a lot of voice breaks(yodelling) and features polyphonic harmonic singing. with some of the singers singing parts that have what seem like deliberate wrong notes to the "haoli" ear--and often have voices singing parts that are non-melodic--

Origins of the music are a bit obscure--the oldest style of Hawaiian singing comes from the chants of the old religion, and is probably as old as the Hawaiians themselves but this music has very few notes, and was either unaccompanied or sung along with drums, and is different from the old style of singing --missionaries came and taught the Hawaiians hymns, and harmonies, and Portuguese and Mexican cowboys taught them some of their stuff, possibly including the falsetto singing that is such a big part of the music--Hawaiian music has been formally taught to Hawaiians since the last century, and there has been a revival in interest in the musical traditions over the last few years, but I don't know how many really try to preserve the old style- Mark will probably be able to add a lot more--