Multi-access edge computing has been considered as a promising solution for enabling computation-intensive yet latency-sensitive applications at resource-constrained wireless devices (WDs). To improve the spectrum efficiency for multi-WD computation offloading, this paper considers non-orthogonal multiple access (NOMA) assisted two-tier multi-access edge computing scenario, which exploits the computation resources of both the edge servers (ESs) and the cloudlet server (CS) deployed at different tiers. In particular, the WDs can offload partial workloads to different ESs simultaneously via NOMA, and the ESs can form a NOMA-group to further offload partially received workloads to the CS for processing. We investigate the total energy consumption minimization problem by jointly optimizing the two-tier offloading decisions, the NOMA transmission duration, and the computation resource allocation. Due to the successive interference cancellation in the NOMA and the coupling effect in two-tier offloading, the formulated optimization problem is strictly non-convex. To address this difficulty, we exploit the hierarchical relationship among the joint optimization variables, and then propose a hybrid deep reinforcement learning (HDRL) algorithm to learn two policies that determine the coupled variables, i.e., the ESs' offloading decisions and the NOMA transmission duration, respectively. Then, the remaining decision variables can be jointly optimized by using the convex optimization methods directly based on the results provided by the HDRL algorithm. Specifically, the HDRL algorithm that uses different policies to determine the coupled variables can converge faster than the existing solutions that learn a single policy to determine all variables. Experimental results are provided to validate the performance of our proposed HDRL algorithm in comparison with two other learning-based algorithms.