The very first reference to OMG has little to do with texting and even technology. An Admiral used the term in a written note to Winston Churchill according to the Oxford English Dictionary. Admiral Fisher used the term and spelled it out in 1917 when emphasizing the razzle dazzle factor of some rumors he apparently was tracking down for Churchill, according to the OED. Admiral Fisher thus, apparently, invented the term OMG.
Later in 1994 in an online chat room the term came up again discussing soap operas.