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In this letter, we propose a novel approach for dynamically selecting an optimal relay mode and optimal transmission power levels in non-orthogonal multiple access wireless networks with relays. To maximize the network throughput, the proposed approach alternates between the one-relay mode and the two-relay mode based on channel state information. For the two-relay mode, we derive novel closed-form results on optimal power control. Unlike in a conventional one-hop network, it is not always optimal to allocate all power to the relay with the largest channel gain in the studied two-hop network. Based on the closed-form results, one could determine the optimal power levels quickly. Simulation results show that the proposed approach could significantly increase the network throughput.