What genre is O Fortuna?

Answer 1

classical, but with a medieval flavouring

In terms of performance genre, it could be called a secular cantata--an extended work for chorus and orchestra in multiple movements, but without an overall narrative. The texts are medieval, but the music is Orff's, written 1935-6. Generally I'd call the musical genre "modern classical," but more specifically, the style of work reminds me of Stravinsky's early period, especially the "primitivist" style of "Rite of Spring."

"O Fortuna" is the first and last movement of Carmina Burana, which Orff himself called a "scenic cantata."