Strained semiconductor nanostructures can be used to make single-photon sources(1), detectors(2) and photovoltaic devices(3), and could potentially be used to create quantum logic devices(4,5). The development of such applications requires techniques capable of nanoscale structural analysis, but the microscopy methods(6-8) typically used to analyse these materials are destructive. NMR techniques can provide non-invasive structural analysis, but have been restricted to strain-free semiconductor nanostructures(9-11) because of the significant strain-induced quadrupole broadening of the NMR spectra(12-14). Here, we show that optically detected NMR spectroscopy can be used to analyse individual strained quantum dots. Our approach uses continuous-wave broadband radiofrequency excitation with a specially designed spectral pattern and can probe individual strained nanostructures containing only 1x10(5) quadrupole nuclear spins. With this technique, we are able to measure the strain distribution and chemical composition of quantum dots in the volume occupied by the single confined electron. The approach could also be used to address problems in quantum information processing such as the precise control of nuclear spins(15-17) in the presence of strong quadrupole effects(18-21).