Looking up the etymology of 'egad' I saw that it is an archaic, euphemistic form of 'O God' or 'Ye God.' I assume this was a one off evolution, and the 'how' was some idiosyncratic shift in the interjection (if it is specifically known how it happened please include in your answer.)
Did this 'egad' catch on in a certain region for some reason, leading it to become more popular? Was it used in some popular form that helped it catch on?
English has a raft of 'minced oaths' to take the place of the original swear words for the sake of politeness. We still use words like darn, ruddy, and flippin' 'eck.
Egad, as well as zounds, 'sblood, struth, gadzooks, etc. are from Elizabethan times. Plays contained plenty of swearing, but in 1606 all oaths on stage were banned. These minced oaths took their place and come down to us in the surviving printed corpus of Elizabethan works.
Full article on wikipedia: http://en.wikipedia.org/wiki/Minced_oath
Etymonline lists the 1670s without attribution, Merriam Webster lists 1673, also without attribution, unfortunately. This date seems to be coming from Geoffrey Hughes' Swearing: A Social History of Foul Language, Oaths & Profanity in English, but I do not have a copy, and I can't chase it down any further. You might check your local library for a copy.
The OED gives the first occurrence as follows:
1673 R. Leigh Transproser Rehears'd 4 Which is very civil I gad.
It cannot very well come from “Ye God”. English-speaking Christians address their god in the 2nd person singular (“thou”), not in the plural (“ye”).
the use of 'Ye' (plural), could be somewhat similar to way we say in Spanish ''Dios'Mio'' =literally, ''My God(s)'', referring to The Three'Persons'of TheTrinity...&being that there was significant French(a Latin-based language like Spanish is..) influence in England, 'tis possible that the grammatical structure and colloquial usage was absorbed along with the phrase regarding 'Your God'...
