Non-orthogonal multiple access (NOMA) and millimeter wave (mmWave) are two key enabling technologies for the fifth-generation (5G) mobile networks and beyond. In this paper, we consider uplink communications with a hybrid beamforming structure and focus on improving the spectral efficiency (SE) and energy efficiency (EE) of mmWave multiple-input multiple-output (MIMO)-NOMA systems with enhanced user grouping and power allocation. Exploiting the directionality feature of mmWave channels, we first propose a novel initial agglomerative nesting (AGNES) based user grouping algorithm by taking advantage of the channel correlations. It is noted that the optimization of the SE/EE is a challenging task due to the non-linear programming nature of the corresponding problem involving user grouping, beam selection, and power allocation. Our idea is to decompose the overall optimization problem into a mixed integer problem comprising of user grouping and beam selection only, followed by a continuous problem involving power allocation and digital beamforming design. To avoid the prohibitively high complexity of the brute-force search approach, we propose two suboptimal low-complexity user grouping and beam selection schemes, the direct AGNES (DIR-AGNES) scheme and the successive AGNES (SUC-AGNES) scheme. We also introduce the quadratic transform (QT) to recast the non-convex power allocation optimization problem into a convex one subject to a minimum required data rate of each user. The continuous problem is solved by iteratively optimizing the power and the digital beamforming. Extensive simulation results have shown that our proposed mmWave-NOMA design outperforms the conventional orthogonal multiple access (OMA) scenario and the state-of-art NOMA schemes.