This paper presents a wireless sensor system (WSS) powered by a strain energy harvester (SEH) through the introduction of an adaptive and energy-aware interface (EAI) for enhanced performance under variable vibration conditions. The interface is realized by an adaptive power management module for maximum power transfer under different loading conditions and an EAI, which manages the energy flow from the storage capacitor to the WSS for dealing with the mismatch between energy demanded and energy harvested. The focus is to realize high harvested power and high efficiency of the system under variable vibration conditions, and an aircraft wing structure is taken as a study scenario. The SEH powered WSS was tested under different peak-to-peak strain loadings from 300 to 600 με and vibrational frequencies from 2 to 10 Hz to verify the system performance on energy generation and distribution, system efficiency, and capability of powering a custom-developed WSS. Comparative studies of using different circuit configurations with and without the interface were also performed to verify the advantages of the introduced interface. Experimental results showed that under the applied loading of 600 με at 10 Hz, the SEH generates 0.5 mW of power without the interface while having around 670% increase to 3.38 mW with the interface, which highlights the value of the interface. The implemented system has an overall efficiency of 70 to 80%, a long active time of more than 1 s, and duty cycle of up to 11.85% for vibration measurement under all the tested conditions.