Hocus-pocus has been around since the early 17th century. The Oxford English Dictionary tells of a conjurer called Hocus-Pocus who used the phrase as part of a faux-Latin incantation during his act: “Hocus pocus, tontus talontus, vade celeriter jubeo.” It’s been plausibly suggested that hocus-pocus is a corruption of the genuine Latin words hoc est enim corpus meum, “for this is my body,” spoken during the consecration of the Roman Catholic Mass when the wine and wafer are said to be transformed into the body and blood of Christ. Some experts, presumably non-Catholic, think hocus-pocus itself was then corrupted into the word hoax.
Abracadabra is a much older term, turning up first in a second-century poem. It was used by the Gnostics, early Christians who placed great stock in esoteric knowledge. The term has been explained as (1) a combination of the Hebrew words ab (“father”), ben (“son”), and ruach acadosch (“holy spirit”); (2) a derivation of the name of one Gnostic leader, Abrasax; or (3) a derivation of Abraxas, a Gnostic word for God, “the source of 365 emanations.” Allegedly the Greek letters for Abraxas add up to 365 when translated according to numerological principles. If you wrote abracadabra on a parchment in a triangular arrangement —
A B R A C A D A B R A
A B R A C A D A B R
A B R A C A D A B
— etc., and hung it around your neck, you’d supposedly be cured of the ague (fever). The over-the-counter remedy of the day, I guess, and probably worked equally well.
Presto, Italian for “quickly,” has been used by conjurers for centuries to command the unseen demons. A possibly related term is prestidigitation, or sleight of hand, which is probably derived from the Latin words for “quick fingers.” (Article by Cecil Adams, The Straight Dope)