I wish I had a better answer to any of those questions, curious, but here is the best I have to offer. The jack in jack shit seems to have unknown provenance, but it may be a phenomenon of the widespread use of jack as an intensifier simply because the word jack has a pleasing or fun sound. See, e.g., Bill Bryson, Made in America: An Informal History of the English Language in the United States 269 (1994) (noting the same uncertain provenance for jackpot and listing numerous other words in which jack seems to have no real meaning). If that were true, then the meaning of the phrase seems to come entirely from the word shit, which could have a slang meaning as "something worthless" or "of no consequence". I have nothing to show when it was first used, though it seems to have originated in the U.S.

As for Jesus H. Christ, it, too, seems to have an uncertain provenance, but one scholar suggested that it might have come from the Greek monogram for Jesus: IHC. Roger Smith, The H of Jesus H. Christ, 69 American Speech 331 (1994). That seems a little too complicated to me, but I'm no scholar in the area, so I'll have to defer to those who know. That said, it seems that it would be another one of those euphonious intensifiers (just like I suggested jack shit might be). Something just sounds better about saying "JEE-zus AECH KRIST", with those three punctuated emphases. Anyway, that's what I've got; I'm sure someone else can find something better.

Ron Draney said:

One not-altogether-serious explanation for "Jesus H Christ" is that the H stands for "haploid".

And where does f###in A Tweety Bird originate?Seems that are ww2 expressions.