The propagation and stability of light three-dimensional Mach 3 and Mach 6 jets of initially cylindrical cross section are explored using the ZEUS-3D code with moderate resolution across the jet diameter. To mimic the behavior of powerful radio jets, which emerge from the centers of active elliptical galaxies through a hot interstellar medium (ISM) and later penetrate into a less dense intracluster medium (ICM), we have set up power-law atmospheres and ISM/ICM interfaces. The simulations are followed to lengths of 35 initial jet radii, and axisymmetry is broken by examining the effects of various inclination angles of the ISM/ICM interface to the jet normal. Increasing the inclination angle produces more asymmetric distributions of vortices in the cocoon, which induce more wiggles and asymmetry in the propagating jet. Even inclination angles of 45 degrees do not produce significant ''refraction'' of the jet, since the initial induced bend is counteracted by extended vortices in the cocoon on the side feeling the lower external densities first. Within the ISM, these three-dimensional jets exhibit rarefaction fans that reflect back from the contact discontinuity between the jet and the ambient medium, yielding compression waves that steepen along the jet axis to form quasi-biconical shocks. Larger inclination angles produce powerful asymmetric reconfining shocks in the jet while it propagates through the ICM. The Mach 3 jets apparently suffer faster growth of higher modes of instabilities. When examined at the ends of our simulations, the trailing portions of the cocoons have collapsed onto the jets.