Significant improvements in the efficiency of optoelectronic devices can result from the exploitation of nanostructures. These require optimal nanocharacterization techniques to fully understand and improve their performance. In this study we employ room temperature cathodoluminescence hyperspectral imaging to probe single GaN-based nanorods containing multiple quantum wells (MQWs) with a simultaneous combination of very high spatial and spectral resolution. We have investigated the strain state and carrier transport in the vicinity of the MQWs, demonstrating the high efficiencies resulting from reduced electric fields. Power-dependent photoluminescence spectroscopy of arrays of these nanorods confirms that their fabrication results in partial strain relaxation in the MQWs. Our technique allows us to interrogate the structures on a sufficiently small length scale to be able to extract the important information.