The detrimental effects of channel aging due to relative movements of user nodes and scatterers in multi-way relay networks (MWRNs) with massive multiple-input multiple-output (MIMO) are investigated. To this end, asymptotic signal-to-interference-plus-noise ratio (SINR) expressions are derived by exploiting a time-varying fading channel model for the case in which the number of antennas at the relay grows without bound. Further, the impact of channel estimation errors and co-channel interference on the performance of MIMO MWRNs with massive MIMO is studied, and thereby, the cumulative effect of pilot contamination and outdated/delayed channel state information due to non-orthogonal pilot sequence reuse and channel aging, respectively, is quantified. The closed-form asymptotic SINRs are then used to derive asymptotic symmetric and asymmetric sum rate expressions. These asymptotic SINR and sum rate expressions are independent of the fast fading effects of the wireless channel. Our results reveal that the transmit power of each user can be scaled down inversely proportional to the relay antenna count for the channel aging only case. Nevertheless, when the system is affected by both pilot contamination and channel aging, the user transmit powers can only be scaled inversely proportional to the square-root of the number of relay antennas. Our results show that the effects of channel aging and pilot contamination significantly degrade the system performance even with relays having very large antenna arrays.