We propose a class of novel energy-efficient multi-cost routing algorithms for wireless mesh networks, and evaluate their performance. In multi-cost routing, a vector of cost parameters is assigned to each network link, from which the cost vectors of candidate paths are calculated using appropriate operators. In the end these parameters are combined in various optimization functions, corresponding to different routing algorithms, for selecting the optimal path. We evaluate the performance of the proposed energy-aware multi-cost routing algorithms under two models. In the network evacuation model, the network starts with a number of packets that have to be transmitted and an amount of energy per node, and the objective is to serve the packets in the smallest number of steps, or serve as many packets as possible before the energy is depleted. In the dynamic one-to-one communication model, new data packets are generated continuously and nodes are capable of recharging their energy periodically, over an infinite time horizon, and we are interested in the maximum achievable steady-state throughput, the packet delay, and the energy consumption. Our results show that energy-aware multi-cost routing increases the lifetime of the network and achieves better overall network performance than other approaches.