Interparticle interactions are self-conflicting rather than cooperative on particular lattices. When such geometrical frustration occurs, charge ordering (CO) can be destabilized into non-trivial charge states such as the recently observed charge glass (CG). A more extreme case is the frustration-induced quantum melting of the CO that has been theoretically proposed. Here, we report d.c. charge transport and noise spectroscopy measurements for a triangular-lattice organic conductor situated close to the CO or CG. Our experiments demonstrate that these materials can host a strange metal with unusual charge dynamics, which we attribute to frustration-induced fluctuations of the CO or CG. Our results also show that the anomalous charge fluctuations can freeze into an insulating state when uniaxial stress is applied, which reduces the geometrical frustration. The present observations suggest the existence of the frustration-induced quantum melting of charges analogous to spin liquids.