This paper presents an effective multi-objective Jaya (EMOJaya) algorithm to solve a multi-objective job-shop scheduling problem, aiming to simultaneously minimise the makespan, total flow time and mean tardiness. A strategy based on grey entropy parallel analysis (GEPA) is developed to assess and select solutions during the search process. To obtain a high-quality reference sequence for GEPA, an opposition-based learning (OBL) strategy is used in parallel. Additionally, the OBL strategy is incorporated into Jaya's search operation and external archive to enhance the search ability and convergence rate of the algorithm. Computational experiments based on 30 benchmark instances with different scales confirm that GEPA and OBL can significantly improve the performance of our proposed EMOJaya. Experimental results also show that EMOJaya is able to outperform three state-of-the-art multi-objective algorithms in solving the problem at hand in terms of convergence, diversity and distribution. Further, EMOJaya can obtain more high-quality scheduling schemes, which provide more and better options for decision makers.