Multi-channel communications can effectively reduce channel competition and interference in a wireless sensor network and thus achieve increased throughput and improved end-to-end delay guarantees with reduced power consumption. However, existing work relies only on a small number of orthogonal channels, resulting in degraded performance when a large number of data flows need to be transmitted on different channels. In this article, we conduct empirical studies to investigate interferences among overlapping channels. Our results show that overlapping channels can also be utilized for improved real-time performance if the node transmission power is carefully configured. In order to minimize the overall transmission power consumption of a network with multiple data flows under end-to-end delay constraints, we formulate a constrained optimization problem to configure the transmission power level of every node and assign overlapping channels to different data flows. Since the optimization problem has an exponential computational complexity, we then present a heuristic algorithm designed based on simulated annealing to find a suboptimal solution. Our extensive empirical results on a 33-mote testbed demonstrate that our algorithm achieves better real-time performance and less power consumption than two baselines, including a scheme using only orthogonal channels.