This article investigates physical layer security of a downlink multiuser orthogonal frequency division multiplexing (OFDM) Internet of Things (IoT) system with an access point communicating with multiple legitimate IoT devices in the presence of multiple eavesdroppers. For coordinating multiuser communication, the orthogonal frequency division multiple access (OFDMA) and time division multiple access (TDMA) are considered. The IoT devices are assumed to support simultaneous wireless information and power transfer (SWIPT) and can use the harvested energy to jam the eavesdroppers based on full-duplex. The resource allocation problems of maximizing the sum secrecy rate for the OFDMA and TDMA systems are investigated. We first consider the scenario that perfect channel state information (CSI) is available and derive suboptimal algorithms based on alternating optimization. Then we consider the scenario that CSI is imperfect and propose heuristic algorithms. The secrecy performances of the OFDMA and TDMA systems with jamming from the SWIPT IoT devices are compared using extensive simulations. It is shown that the secrecy performance of the OFDMA system is superior over the TDMA system. It is also shown that the algorithm with imperfect CSI is inferior over the algorithm with perfect CSI, but it can outperform the benchmark algorithm with perfect CSI and without jamming.