Repost from reddit:
http://imgur.com/XOG8CQn
"Years ago, the Lin Kuei Grandmaster determined that his assassin clan would be more effective by eliminating their human weaknesses. They would adopt cybernetic bodies and technologically enhanced minds. In preparation, the Grandmaster ordered all members to submit to tests, during which their physical and mental data was secretly recorded and stored in an offsite database. After Sub-Zero eliminated all cyber-Lin Kuei, Special Forces discovered their hidden data storage site. They brought the drives to a secret S-F weapons lab, then downloaded several files into a test body. The consciousness of Sektor, Cyrax and Smoke somehow intermingled and brought the body to life. The "Triborg" wiped the lab clean of human occupants -- and now seeks to eliminate all organic life."
So that pretty much sums it up. Sometime before the cyber initiative started the grandmaster basically downloaded the mental/physical data of Smoke (and the other Lin Kuei) which is how it's possible for smoke to exist this way. So in reality it seems it isn't Smoke, but rather just his image imprinted on Triborg. Same goes for Sektor and Cyrax and I'm guessing Sub-Zero but it doesn't mention how he ties in with the other three, at least in terms of Triborg, I'm guessing he just happened to have downloaded Sub-Zero's image along with the other three.
Actually thinking about it more now, Triborg is kind of similar to Combot from Tekken. Point is that he is able to use different fighting styles that he has stored in his database (which happen to be Lin Kuei members) but on top of that he also takes on their visual appearance.