With the rapid development of Internet of Things, Smart Manufacturing, and Telematics, edge devices are facing increasing computational demands and limited resources. Efficient multi-objective task offloading in dynamic network environments has become a key challenge in edge computing. This paper proposes a Proximal Policy Optimization algorithm based on Hybrid Prioritized Experience Replay (HyPER-PPO) for multi-objective optimization of task offloading decisions. The offloading process is modeled as a multi-objective Markov decision process (MOMDP), with a dynamic weight adjustment mechanism to adaptively balance delay and energy consumption. To address sample inefficiency in Proximal Policy Optimization, we introduce a hybrid prioritized replay mechanism based on Temporal Difference (TD) error and Generalized Advantage Estimation (GAE), enabling the reuse of high-value historical experiences. Additionally, an Importance Sampling (IS) weight is applied to correct bias caused by non-uniform sampling, improving update stability. Experimental results show that Multi-Objective HyPER-PPO significantly outperforms the UCB1, SPEA/R, and NSGA-III algorithms, achieving$\text{7 3 \%}$lower task latency and$\text{5 6 \%}$lower energy consumption in complex MEC environments. The proposed approach offers a scalable and effective solution for intelligent task offloading in real-world edge computing systems.