This paper aims to investigate the issue of energy management for multi-energy communities with diversified energy consumer profiles. Since the energy consumers have their points of parity and differences in their demographic, psychological and behavioral traits, it is assumed that the energy management scheme should be capable of meeting their actual needs instead of just reducing the energy bills as conventional researches do. Hence, this paper proposes a multi-objective energy management strategy for diversified energy consumers to achieve energy-tailoring. Firstly, a novel entropy based energy consumer clustering approach is proposed for optimal consumer segmentation. Following that, four multi-objective energy management models are proposed to achieve the goal of energy bill minimization, maximization of green energy usage, reduction of energy losses and optimization of energy usage quality. Meanwhile, the strategy to achieve priority-based coordination of the four objectives is developed. To this end, a multi-agent system is developed to perform the optimization model. Simulation case studies are conducted to validate the effectiveness of the proposed method. Numerical results have shown that the proposed approach can achieve co-optimization of the four objectives, and the tradeoffs caused by the competing interest groups are maintained at a low level.