Measurements of light emission from GaN nanorods of diameter between 80 and 350 nm, containing either a three-well multiple InGaN quantum well or a single quantum well, have been performed by photoluminescence (PL) and cathodoluminescence (CL) hyperspectral imaging. The PL underwent a Stark shift to the blue as the nanorod diameter was reduced, indicating substantial relaxation of the compressive strain in the quantum wells. The intensity of the nanorod emission per unit area can exceed that of the planar starting material. The CL measurements revealed that the wavelength of the quantum well emission varied with radial position in the nanorod. Simulations by a modal expansion method revealed that the light extraction efficiency varies with radial position and the variation is dependent on nanorod diameter. Finite difference time domain simulations showed that Bloch mode formation in the buffer layer below the nanorods impacts on the light extraction.