In this paper, we propose a joint dynamic power control and user pairing algorithm for power-efficient and delay-constrained hybrid multiple access systems. In a hybrid multiple access system, user pairing determines whether the transmitter serves as a certain user by orthogonal multiple access (OMA) or non-orthogonal multiple access (NOMA). The proposed optimization framework minimizes the long-term time-average transmit power expenditure while reducing the queuing delay and guaranteeing the minimum time-average data rates. The proposed technique observes both channel and queue state information and adjusts queue backlogs to avoid an excessive queueing delay by appropriate user pairing and power allocation. Furthermore, the flexible use of resources is captured in the proposed algorithm by employing NOMA. The data-intensive simulation results show that the proposed scheme for power allocation and user scheduling achieves a balance among multiple performance goals, i.e., power efficiency, queueing delay, and data rate.