"Listening to Brahms" by Suzy McKee Charnas, first published in the September 1986 Omni (scanned copy here), reprinted under these covers.
About a guy who's stranded orbiting (?) an alien planet after humanity has been wiped out.
The narrator (and a couple of fellow astronauts) was in cryosleep orbiting Earth when the alien Kondrai came:
I sit looking through the viewplate at Earth, such as it is. I know what the lizards say is true, but I don't think I really believe it. I think mostly that I'm dead or having a terrible dream.
The aliens take them back to their home planet:
Entry 3: Captain Midnight says now that we're all up he would be honored beyond expression if we would consent to come back to Kondra with him and his crew in their ship. Kondra is their name for their world. Chu says she's worked out where and what it is in our terms, and she keeps trying to show me on the star charts. I don't care. I came up here to do studies on cryogenic nutrition in space, not to look at star charts.
Toward the end of the story, you find out there's a "cult" springing up among the alien youth that human souls from the destroyed Earth are transmigrating to the alien world and reincarnating there.
Entry 20: They are saying that the reason there's so much crime and violence on Kondra isn't because of the population explosion at all. Some snake who calls himself Swami Nanda has worked out how the demographic growth is only a sign of the underlying situation.
According to him Kondra made an "astral agreement" to take in not only us living human survivors but the souls of all the dead of Earth. Earth souls on the astral plane seeing that there were soon going to be no more human bodies on Earth to get born into, sent out a call for new bodies and a new world to inhabit. The Kondran souls on the astral plane, having pretty much finished their work on the material world of Kondra, agreed to let human souls take over the physical plant here, as it were. Now the younger generation is all Earth souls reborn as Kondrai on this planet, and they're recreating conditions familiar to them from Earth.
The man also listens to classical music a lot -- nothing with human voices though.
Entry 5: Sibelius, Symphony No. 2 in D, Op. 43; Tchaikovsky, Variations on a Rococo Theme, Op. 33; Rachmaninoff, Symphonic Dances, Op. 45; Mozart, Clarinet Quintet in A Major, K581; Sibelius, Symphony No. 2 in D, Op. 43; Sibelius, Symphony No. 2 in D, Op. 43