Biological nanoparticles are important targets of study, yet their small size and tendency to aggregate makes their heterogeneity difficult to profile on a truly single-particle basis. Here we present a label-free system called 'Raman-enabled nanoparticle trapping analysis' (R-NTA) that optically traps individual nanoparticles, records Raman spectra and tracks particle motion to identify chemical composition, size, and refractive index. R-NTA has the unique capacity to characterize aggregation status and absolute chemical concentration at the single-particle level. We validate the method on NIST standards and liposomes, demonstrating that R-NTA can accurately characterize size and chemical heterogeneity, including determining combined morpho-chemical properties such as the number of lamellae in individual liposomes. Applied to extracellular vesicles (EVs), we find distinct differences between EVs from cancerous and noncancerous cells, and that knockdown of the TRPP2 ion channel, which is pathologically highly expressed in laryngeal cancer cells, leads the EVs to more closely resemble EVs from normal epithelial cells. Intriguingly, the differences in EV content are found in small subpopulations of EVs, highlighting the importance of single-particle measurements. These experiments demonstrate the power of the R-NTA system to measure and characterize the morpho-chemical heterogeneity of bionanoparticles.