Senabling a satellite network with edge computing capabilities, SEC provides users with a full range of computing service. In this paper, we construct a multi-objective optimization model for task offloading with data-dependent constraints in an SEC network and aim to achieve optimal tradeoffs among energy consumption, cost, and makespan. However, dependency constraints between tasks may lead to unexpected computational delays and even task failures in an SEC network. To solve this, we proposed a Petri-net-based constraint amending method with polynomial complexity and generated offloading results satisfying our constraints. For the multiple optimization objectives, a strengthened dominance relation sort was established to balance the convergence and diversity of nondominated solutions. Based on these, we designed a multi-objective wolf pack search (MOWPS) algorithm. A series of adaptive mechanisms was employed for avoiding additional computational overhead, and a Lamarckian-learning-based multi-neighborhood search prevents MOWPS from becoming trapped in the local optimum. Extensive computational experiments demonstrate the outperformance of MOWPS for solving task offloading with data-dependent constraints in an SEC network.