Remember Jessica Rabbit singing in Who Framed Roger Rabbit?

That particular style of singing is referred to as "Torch singing" for the very seductive way it is delivered. The music is generally old well known favorites from all of the music styles you described.

That was Kathleen Turner singing in that movie. I would probably call that style of music jazz/blues as blues is a type of jazz. Some female singers that sing in that style are Diana Krall, Bessie Smith, Billy Holiday, Dorothy Dandridge, and a host of others.

I believe it was classified as jazz, and Natile Cole sings like that