This work considers multiple user power-domain non-orthogonal multiple access (NOMA)based downlink (DL) and uplink (UL) communication systems with potentially dissimilar fading links for all the users that can follow one of several possible distributions such as Rayleigh, Rician, Nakagami-m, Nakagami-q, κ - μ, η - μ, Nakagami-lognormal. The presented analysis, which is based on approximating the probability density function (PDF) of the channel gain as a sum of Gamma distributions, is sufficiently general and applicable in a multitude of NOMA scenarios. For both the UL and DL, closed-form expressions are determined for the outage probability at the users considering both statistical channel state information (CSI)-based as well as instantaneous CSI-based ordering techniques. Analytical expressions for the outage probability and the ensuing diversity orders have also been obtained for the NOMA DL system at high SNRs. Furthermore, similar expressions for the outage probability and outage floor for the NOMA UL system have been derived at high SNRs. Finally, simulation results have been presented to authenticate the analytical results derived and provide insights into the NOMA system performance.