In mobile opportunistic networks (MONs), a large number of intelligent devices carried by moving people can conduct message transmission without the support of communication infrastructures. Routing is one of the concerning and challenging research hotspots in MONs because of nodes' mobility, intermittent connectivity, limited nodes' energy, and the dynamic changing quality of the wireless channel. However, only one or several of the above factors are considered in most current routing methods. Moreover, owing to the high mobility of nodes, it is particularly important to decide the time when to make the forwarding decision and which nodes can be selected as the relay nodes. Additionally, due to the dynamic changing quality of the wireless channel, the predetermined relay nodes for the next hop may not receive the message. In this paper, we propose a novel energy-efficient probabilistic routing method for MONs, in which energy and mobility of nodes and the quality of wireless channel are all taken into account. Firstly, we explore the regularity of nodes' mobility and the encounter probability among nodes to decide the time when to forward messages to other nodes. Secondly, by maintaining the energy fairness among nodes, the network lifetime can be prolonged. Thirdly, by fully taking the dynamic changing quality of the wireless channel into consideration, the retransmission number of messages can be effectively reduced. Additionally, we adopt a forwarding authority transfer policy for each message, which can effectively control the number of replicas for each message. The extensive simulation results show that the proposed method outperforms the existing routing algorithms in terms of the delivery ratio and the overhead ratio.