Optical Sensors - Enterprise's optical sensors have a resolution of greater than 1-cm from 500-km, enough to see specific facial features of the natives, including their cranial ridges. (Civilization)
Orbit - SEE: Geosynchronous Orbit.
Orbital Six - the designation of the pod that Trip and Archer used to view the outside of the ship prior to its launch. At one point Trip wasn't paying attention to the controls and it drifted into the bottom of the saucer where it "scratched the paint". (Broken Bow)
Orbital Engineer - Daniel's cover story included a nonexistant brother who was an orbital engineer at Jupiter Station. (Cold Front)
Omega training mission - Tucker's EV pack malfunctioned on Titan during the omega training mission, inducing nitrogen-narcosis. Archer managed to talk him out of taking his helmet off, thus saving his life. It is not known if this was the final exercise in Starfleet training, or training for a specific mission to somewhere called Omega, or just an arbitrary letter designation for a routine training mission. (Strange New World)