Villa studied at the Mateu Conservatoire of Havana. He worked as a chauffeur and played piano for silent films until his friend Rita Montaner took him on as an accompanist in the early 1930s. After Montaner returned to Cuba, Villa remained in Mexico and developed an original performance style as a pianist and singer. He was an elite rather than a popular figure, a sophisticated cabaret stylist known for ironic patter, subtle musical interpretation, with a repertoire that included songs in French, English, Catalan, Portuguese and Italian. He toured widely in Europe and the Americas, and his friends included Andres Segovia and Pablo Neruda. He was black and gay, self-confident in his personality, and was accepted for what he was: a memorable talent.
He was the subject of a 2003 documentary which includes interviews with fellow musicians, friends, relatives, and experts.