Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) is a novel technology which enables the full-space coverage. In this letter, a multi-active STAR-RIS-aided system using non-orthogonal multiple access in an uplink transmission is considered, where the second-order reflections among multiple active STAR-RISs assist the transmission from the single-antenna users to the multi-antenna base station. Specifically, the total sum rate maximization problem is solved by jointly optimizing the active beamforming, power allocation, transmission and reflection beamforming at the active STAR-RISs, and user-active STAR-RIS assignment. To solve the non-convex optimization problem, a novel deep reinforcement learning algorithm is proposed which integrates Meta-learning and deep deterministic policy gradient (DDPG), denoted by Meta-DDPG. Numerical results reveal that our proposed Meta-DDPG algorithm outperforms the DDPG algorithm with $19\%$ improvement, while second-order reflections among multi-active STAR-RISs provide $74.1\%$ enhancement in the total data rate.