This article investigates the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted nonorthogonal multiple access (NOMA) systems with one cooperative jammer and dual eavesdroppers. To guarantee the uplink secure transmission, we maximize the sum secrecy rate under both the perfect and imperfect channel state information (CSI) by jointly optimizing the channel allocation, transmit power, and coefficient matrices. For the problem with perfect CSI, a deep reinforcement learning algorithm is proposed based on the deep deterministic policy gradient (DDPG) framework. Then, by introducing the arbitrary distorted noise to the state space, the proposed algorithm is extended to solve the problem under imperfect CSI without causing additional computational complexity. Simulation results illustrate that: 1) the symmetry of STAR-RIS results in severe information leakage and the sum secrecy rate further degrades when the dual eavesdroppers collaborate with each other; 2) the STAR-RIS with independent phase shift can achieve higher sum secrecy rate than that with coupled phase shift, while the performance gap is trivial when there are fewer STAR-RIS elements; and 3) our proposed algorithm can compensate for the impacts of the imperfect CSI, and the sum secrecy rate decreases with the increase of CSI uncertainty.