We investigate the integration of an active reconfigurable intelligent surface (ARIS) with nonorthogonal multiple access (NOMA) to enhance the secrecy performance and the security capabilities in Internet of Things (IoT) systems. The system model incorporates ARIS and NOMA, allowing for improved power allocation and higher security. In particular, the physical-layer security of an ARIS-NOMA system is investigated when the system is subject to eavesdropping by a malicious user in a user pair group. To provide real-world impact, we examine the main system performance metrics, including the connection outage probability, the secrecy outage probability (SOP), and the strictly positive secrecy capacity, which are important guidelines in evaluating the system's reliability, security, and achievable secrecy rates. We evaluate the impact of distances between the ARIS, the eavesdropper, and the base station on the SOP. We derive the optimal power allocation factors in the NOMA scheme, which provides insights into the system design and parameter adjustment to achieve robust and secure operation. In comparison to a benchmark model using the orthogonal multiple access, we show ARIS-NOMA is a promising solution to further enhance security and secrecy in IoT networks.