This paper introduces the Active Simultaneously Transmitting and Reflecting Surface Assisted Non-Orthogonal Multiple Access (ASTARS-NOMA) networks, which leverage the capabilities of ASTARS to enhance communication performance. The ASTARS is designed to control the phase shifts of cascaded channels to align the phases at pairing users, enabling better signal alignment and improved performance. The paper uses stochastic geometry to model the spatial positions of users and derives closed-form and asymptotic expressions for the outage probability and ergodic data rate of ASTARS-NOMA networks under perfect and imperfect successive interference cancellation (pSIC/ipSIC). The diversity orders and multiplexing gains for ASTARS-NOMA are analyzed, showing that the diversity orders are proportional to the number of ASTARS elements. The system throughputs of ASTARS-NOMA are evaluated in both delay-tolerant and delay-limited transmission modes, demonstrating that ASTARS-NOMA outperforms ASTARS-assisted orthogonal multiple access (ASTARS-OMA) in terms of outage probability and ergodic data rate. The results show that increasing the power amplification factors can further reduce the outage probability of ASTARS-NOMA. The paper also compares the performance of ASTARS-NOMA with other networks, showing that ASTARS-NOMA achieves better performance in both delay-limited and delay-tolerant transmission modes. The analysis confirms that ASTARS-NOMA is a promising technology for combating multiplicative fading loss and achieving full-space smart radio environments.This paper introduces the Active Simultaneously Transmitting and Reflecting Surface Assisted Non-Orthogonal Multiple Access (ASTARS-NOMA) networks, which leverage the capabilities of ASTARS to enhance communication performance. The ASTARS is designed to control the phase shifts of cascaded channels to align the phases at pairing users, enabling better signal alignment and improved performance. The paper uses stochastic geometry to model the spatial positions of users and derives closed-form and asymptotic expressions for the outage probability and ergodic data rate of ASTARS-NOMA networks under perfect and imperfect successive interference cancellation (pSIC/ipSIC). The diversity orders and multiplexing gains for ASTARS-NOMA are analyzed, showing that the diversity orders are proportional to the number of ASTARS elements. The system throughputs of ASTARS-NOMA are evaluated in both delay-tolerant and delay-limited transmission modes, demonstrating that ASTARS-NOMA outperforms ASTARS-assisted orthogonal multiple access (ASTARS-OMA) in terms of outage probability and ergodic data rate. The results show that increasing the power amplification factors can further reduce the outage probability of ASTARS-NOMA. The paper also compares the performance of ASTARS-NOMA with other networks, showing that ASTARS-NOMA achieves better performance in both delay-limited and delay-tolerant transmission modes. The analysis confirms that ASTARS-NOMA is a promising technology for combating multiplicative fading loss and achieving full-space smart radio environments.