This paper aims to design and evaluate the performance of multi-cluster multi-user dual-polarized massive multiple-input multiple-output (MIMO) systems with non-orthogonal multiple access (NOMA).Assuming the downlink mode in which a single base station communicates with multiple users, with all terminals being equipped with multiple co-located dual-polarized antennas, two precoder designs are proposed: (i) the first one aims to maximize the number of user groups that are simultaneously served within a cluster; and (ii) the second approach aims to provide further improvements compared to the first one by exploring polarization diversity. Closed-form expressions for the outage probability are derived for both approaches, based on which the respective asymptotic studies are carried out and the diversity gains are determined. The ergodic sum-rates are also derived. Representative numerical examples are presented along with insightful discussions. For instance, our results show that the proposed dual-polarized MIMO-NOMA designs outperform conventional single-polarized systems, even for high cross-polar interference. Simulation results are plotted to corroborate the analytical framework and analysis.