The separate receiver architecture with a time- or power-splitting mode, widely used for simultaneous wireless information and power transfer (SWIPT), has a major drawback: Energy-intensive local oscillators and mixers need to be installed in the information decoding (ID) component to downconvert radio frequency (RF) signals to baseband signals, resulting in high energy consumption. As a solution to this challenge, an integrated receiver (IR) architecture has been proposed, and, in turn, various SWIPT modulation schemes compatible with the IR architecture have been developed. However, to the best of our knowledge, no research has been conducted on modulation scheduling in SWIPT-based IoT sensor networks while taking into account the IR architecture. Accordingly, in this paper, we address this research gap by studying the problem of joint scheduling for unicast/multicast, IoT sensor, and modulation (UMSM) in a time-slotted SWIPT-based IoT sensor network system. To this end, we leverage mathematical modeling and optimization techniques, such as the Lagrangian duality and stochastic optimization theory, to develop an UMSM scheduling algorithm that maximizes the weighted sum of average unicast service throughput and harvested energy of IoT sensors, while ensuring the minimum average throughput of both multicast and unicast, as well as the minimum average harvested energy of IoT sensors. Finally, we demonstrate through extensive simulations that our UMSM scheduling algorithm achieves superior energy harvesting (EH) and throughput performance while ensuring the satisfaction of specified constraints well.