Etymology
The expression dates to at least the late 19th century, although according to Mark Twain it was already old in 1850, and likely originates with the ancient Christian three-letter symbolism IHS (the Christogram). (Smith 1994, p. 332)
Using the name of Jesus Christ as an oath has been common for many centuries, but the precise origins of the letter H in the expression Jesus H. Christ are obscure. While many explanations have been proposed, some serious and many humorous, the most widely accepted derivation is from the divine monogram of Christian symbolism. The symbol, derived from the first three letters of the Greek name of Jesus (Ιησούς), is transliterated IHS, IHC, JHS or JHC. Since the transliteration IHS gave rise to the backronym Iesus Hominum Salvator (Latin for "Jesus savior of men"), it is plausible that JHC similarly led to Jesus H. Christ. (Smith 1994, pp. 332-3)
http://en.wikipedia.org/wiki/Jesus_H._Christ#Etymology
Dear W.:
The H stands for Harold, as in, "Our Father, who art in heaven, Harold be thy name" (snort).
Actually, I've heard numerous explanations for the H over the years. The first is that it stands for "Holy," as in Jesus Holy Christ, a common enough blasphemy in the South, abridged to H by fast-talking Northerners. Other colorful Southern epithets include Jesus Hebe Christ and Jesus Hebrew Christ, which abbreviate the same way. The drawback of this account is that it is so boring I can barely type it without falling asleep. Luckily, the other theories are more entertaining:
(1) It stands for "Haploid." This is an old bio major joke, referring to the unique (not to say immaculate) circumstances of Christ's conception. Having no biological father, J.C. was shortchanged in the chromosome department to the tune of one half. Ingenious, I'll admit, but whimsy has no place in a serious investigation such as this.
(2) It recalls the H in the IHS logo emblazoned on much Christian paraphernalia. IHS dates from the earliest years of Christianity, being an abbreviation of "Jesus" in classical Greek characters. The Greek pronunciation is "Iesous," with the E sound being represented by the character eta, which looks like an H. When the symbol passed to Christian Romans, for whom an H was an H, the unaccountable character eventually became accepted as Jesus's middle initial.
(3) Finally, a reader makes the claim that the H derives from the taunting Latin inscription INRH that was supposedly tacked on the cross by Roman soldiers: Iesus Nazarenus, Rex Hebrei (Jesus the Nazarene, King of the Hebrews). Trouble is, the inscription is usually given as INRI: Iesus Nazarenus, Rex Iudaeorum (J.C., King of the Jews).
Nonetheless, this is the kind of creative thinking I like to see from my Teeming Millions. With every passing day, my mission on this earth comes closer to completion.
— Cecil Adams
http://www.straightdope.com/columns/read/30/why-do-folks-say-jesus-h-christDisclaimer... I have no evidence to support the accuracy (or inaccuracy), of the cited articles.