TERRIFYING AND EERIE things happen in the world of the occult, but few can be more bizzare than Falling Angel (Harcourt, Brace, $8.95) - a diabolical coupling of the hard-boiled detective story with the novel of the supernatural. Or, as one of the blurbs on the jacket puts it: "the result of mating The Big Sleep with The Exorcist."

The union has produced a fiendish hybrid. Falling Angel is a compelling, page-turning story in the best private-eye tradition, with brilliantly nightmarish scenes of black magic and voodoo. Unfortunately, Hjortsberg's story is repulsively disfigured by some cheap bows to sensationalism, although he does come awfully close to carrying off this gumshoe-cum-supernatural thriller.

It is Friday, March 13, 1959, and Harry Angel, a New York private eye, has just been hired to trace Johnny Favorite, who'd been a big singing sensation until he went off to World War II and came back a human vegetable. From the opening page, Hjortsberg captures the mood of the period, as well as the appropriate hard-edged style.

"I spun my chair around and stared out at Times Square. The Camels spectacular on the Claridge puffed fat steam smoke rings over the snarling traffic. The dapper gentleman on the sign, mouth frozen in a round O of perpetual surprise, was Broadway's harbinger of spring. Earlier in the week, teams of scaffold-hung painters transformed his winter homburg and chesterfield overcoat into a seersucker and panama straw, not as poetic as the Capistrano swallows but it got the message across."

Angel's search takes him to Harlem, off-season Coney Island, a voodoo ritual in Central Park, and a black mass sacrifice in an abandoned underground subway station. The way is strewn with bodies. No one is simply murdered; victims are tortured and mutilated in such unpleasant ways that one (almost) wonders how Hollywood will make the movie.

The final shocker is spellbinding. But once the effect wears off, the reader may come up with an empty feeling. This, I confess, may be the parochial complaint of a mystery fan who grasps for any shred of logic in a solution and expects the case to be cracked.