We report the discovery and orbit determination of 14 trans-Neptunian objects (TNOs) from the ESSENCE Supernova Survey difference imaging dataset. Two additional objects discovered in a similar search of the SDSS-II Supernova Survey database were recovered in this effort. ESSENCE repeatedly observed fields far from the Solar System ecliptic (-21 deg < beta < -5 deg), reaching limiting magnitudes per observation of I~23.1 and R~23.7. We examine several of the newly detected objects in detail, including 2003 UC_414 which orbits entirely between Uranus and Neptune and lies very close to a dynamical region that would make it stable for the lifetime of the Solar System. 2003 SS_422 and 2007 TA_418 have high eccentricities and large perihelia, making them candidate members of an outer class of trans-Neptunian objects. We also report a new member of the extended or detached scattered disk, 2004 VN_112, and verify the stability of its orbit using numerical simulations. This object would have been visible to ESSENCE for only ~2% of its orbit, suggesting a vast number of similar objects across the sky. We emphasize that off-ecliptic surveys are optimal for uncovering the diversity of such objects, which in turn will constrain the history of gravitational influences that shaped our early Solar System.