We first conceive a novel transmission protocol for a multi-relay multiple-input--multiple-output orthogonal frequency-division multiple-access (MIMO-OFDMA) cellular network based on joint transmit and receive beamforming. We then address the associated network-wide spectral efficiency (SE) and energy spectral efficiency (ESE) optimization problems. More specifically, the network's MIMO channels are mathematically decomposed into several effective multiple-input--single-output (MISO) channels, which are essentially spatially multiplexed for transmission. Hence, these effective MISO channels are referred to as spatial multiplexing components (SMCs). For the sake of improving the SE/ESE performance attained, the SMCs are grouped using a pair of proposed grouping algorithms. The first is optimal in the sense that it exhaustively evaluates all the possible combinations of SMCs satisfying both the semi-orthogonality criterion and other relevant system constraints, whereas the second is a lower-complexity alternative. Corresponding to each of the two grouping algorithms, the pair of SE and ESE maximization problems are formulated, thus the optimal SMC groups and optimal power control variables can be obtained for each subcarrier block. These optimization problems are proven to be concave, and the dual decomposition approach is employed for obtaining their solutions. Relying on these optimization solutions, the impact of various system parameters on both the attainable SE and ESE is characterized. In particular, we demonstrate that under certain conditions the lower-complexity SMC grouping algorithm achieves 90% of the SE/ESE attained by the exhaustive-search based optimal grouping algorithm, while imposing as little as 3.5% of the latter scheme's computational complexity.