Latency and reliability capabilities of currently available fourth-generation (4G) wireless networks paved the path towards massively connected devices requiring much lower latency and much higher reliability. In the fifth-generation (5G) wireless networks, the concept of ultra-reliable and low-latency communications (URLLC) is introduced to fulfill these demands. URLLC aims to deliver short packets with 1 ms latency with a reliability rate of 99.999%. The cellular Internet of Things (IoT) is a framework for conceptualizing such massive connectivity while addressing fundamental challenges such as the ever-increasing number of interconnected devices, latency constraints, and high-throughput demands. One of the challenging tasks for cellular IoT applications is the delivery of deadline-constrained information to densely deployed IoT devices. Increasing demand for delivering timing-critical information in cellular IoT networks poses a URLLC-oriented challenge for both academia and industry. With this motivation, this thesis aims to develop techniques for reliably transferring short packets to densely deployed devices within a given deadline. In this thesis, we address the problem of latency-constrained communications with strict deadlines under average power constraint using Multiple Access (MA) schemes. The first MA scheme considered in the thesis is Hybrid MA, which consists of both Orthogonal MA (OMA) and power domain Non-Orthogonal MA (NOMA) as transmission scheme options. The second MA scheme studied in the thesis is Rate-Splitting Multiple Access (RSMA), which generalizes OMA, NOMA and Space-Division MA (SDMA) schemes. We maximize the timely throughput, which represents the average number of successfully transmitted packets before deadline expiration, where expired packets are dropped from the buffer. We use Lyapunov stochastic optimization methods to develop a dynamic power assignment algorithm for minimizing the packet drop rate while satisfying time average power constraints. Moreover, we propose a flexible packet dropping mechanism called Early Packet Dropping (EPD) to detect likely to become expired packets and drop them proactively. Finally, we propose a simple heuristic to reduce the computational load of the proposed algorithm. Numerical results show that Hybrid MA improves the timely throughput compared to conventional OMA by up to 46% and on average by more than 21%. With EPD, these timely throughput gains improve to 53% and 24.5%, respectively. Utilization of RSMA with EPD further improves timely throughput by up to 5.95% and on the average by about 3.12% compared to Hybrid MA with EPD. Simulation results indicate that the proposed heuristic significantly reduces the computational load at the cost of a small loss in the timely throughput performance.