Non-orthogonal multiple access (NOMA) techniques have emerged in the past years as a solution to approximate the throughput performance of wireless communications systems to their theoretical capacity region. We consider in this paper an optimization-based model for multicast device-to-device (MD2D) communications where the channels are not orthogonal and maybe (partially or fully) shared among the transmitters in each cluster. This setting leads naturally to the introduction of NOMA transmitters and receivers who use successive interference cancellation(SIC) to separate the superposed signals. To analyze the role of NOMA in MD2D, its performance impact, potential performance gains and possible shortcomings, we formulate a model that includesSIC operations in the decoders, so that higher rates can be attained when several sources transmit on the same channel(s). We also investigate the energy efficiency of the network (global and max-min)through a dynamic power control algorithm and present a centralized and a semi-distributed solution to these optimization problems. Through numerical simulations, we show that NOMA is able to improve both the sum-rate and the max-min rate of a MD2D network even from a small degree of resource sharing. Furthermore, these gains also improve the global energy efficiency on the network,but not always the max-min energy efficiency of the devices.