Metal oxide heterostructure assemblies made of ZnO-Co₃O₄ core–shell nanowires enable high-performance self-powered optoelectronic devices with potential applications in wireless, autonomous, low maintenance medical implants or environmental sensors. Surprisingly, the experimental study of the single core–shell heterostructures forming the assembly was never reported until now. We unveil the transport phenomena occurring in individual ZnO-Co₃O₄ core–shell nanowires by engineering ionic liquid-gated nanotransistors. The nanostructures are isolated on fabrication substrates and equipped with a set of metallic electrodes probing selectively different sections of the nanowire, in three different configurations labelled core–core, shell–shell and core–shell. The observed electrical responses reflect the properties of the ZnO core, the Co shell and the core–shell heterojunction. The ultrahigh capacitive coupling of the ionic liquid to the nanowire and its conformal feature reveal multiple transport regimes in the same nanodevice: the core, the shell and the core–shell heterojunction act as a linear, nonlinear, and rectifying nanoelectronic components, respectively. This work shines light on the transport properties of individual metal oxide nanowire heterostructures employed in self-powered optoelectronics, suggesting potential applications as multifunctional nanoelectronic components. The methodologies developed in this research set the benchmark for the investigation of nanoscale building blocks of functional semiconductor nanomaterial assemblies for electronic and optoelectronic applications.