Elastic and electrical conductive sponges are attracting materials for energy storage and energy harvest devices. In this study, we have demonstrated that a flexible and durable Cu doped PDMS sponge (Cu) can be adopted as electrodes for triboelectric nanogenerators (TENG) and flexible supercapacitors (SC). The Cu sponge loading with polypyrrole (PPy) was newly applied as single-electrode TENG for the first time. The outputs of the TENG were tuned by varying the PPy content or by combining with PDMS sponge. Due to the feasibility of changing the PPy content in the Cu@PPy sponges, this study offers a facile way to enhance the performance of TENG from the material itself with a tunable manner. Moreover, this study potentiates a better understanding of the triboelectricity produced by the TENG from the view of materials. The Cu@PPy sponges were further utilized as electrodes for all solid-state symmetrical SCs, in which the Cu sponge and PPy showed a synergistic effect on promoting the stability and performance of the SC. The SC exhibits lightweight, good capacitance, high flexibility, excellent mechanical and long-term stability, which is suitable for wearable energy storage devices. For the application of the TENG and the SC, a self-powered hybrid device was assembled, which provides a prospect for integrated devices. As a summary, we reported a new metal sponge based TENG and self-powered hybrid device, which demonstrated our study provides new opportunities for elastic multifunctional power sources and potential applications in wearable electronics.