Our deteriorating civil infrastructure faces the critical challenge of long-term structural health monitoring for damage detection and localization. In contrast to existing research that often separates the designs of wireless sensor networks and structural engineering algorithms, this paper proposes a cyber-physical codesign approach to structural health monitoring based on wireless sensor networks. Our approach closely integrates 1) flexibility-based damage localization methods that allow a tradeoff between the number of sensors and the resolution of damage localization, and 2) an energy-efficient, multilevel computing architecture specifically designed to leverage the multiresolution feature of the flexibility-based approach. The proposed approach has been implemented on the Intel Imote2 platform. Experiments on a simulated truss structure and a real full-scale truss structure demonstrate the system's efficacy in damage localization and energy efficiency.