Multiple-input multiple-output (MIMO) systems exploit spatial diversity to facilitate multi-user communications with high spectral efficiency by beamforming. As MIMO systems utilize multiple antennas and radio frequency (RF) chains, they are typically costly to implement and consume high power. A common method to reduce the cost of MIMO receivers is utilizing less RF chains than antennas by employing hybrid analog/digital beamforming (HBF). However, the added analog circuitry involves active components whose consumed power may surpass that saved in RF chain reduction. An additional method to realize power-efficient MIMO systems is to use low-resolution analog-to-digital converters (ADCs), which typically compromises signal recovery accuracy. In this work, we propose a power-efficient hybrid MIMO receiver with low-quantization rate ADCs, by jointly optimizing the analog and digital processing in a hardware-oriented manner using task-specific quantization techniques. To mitigate power consumption on the analog front-end, we utilize efficient analog hardware architecture comprised of sparse low-resolution vector modulators, while accounting for their properties in design to maintain recovery accuracy and mitigate interferers in congested environments. To account for common mismatches induced by non-ideal hardware and inaccurate channel state information, we propose a robust mismatch aware design. Supported by numerical simulations and power analysis, our power-efficient MIMO receiver achieves comparable signal recovery performance to power-hungry fully-digital MIMO receivers using high-resolution ADCs. Furthermore, our receiver outperforms the task-agnostic HBF receivers with low-rate ADCs in recovery accuracy at lower power and successfully copes with hardware mismatches.