We investigate the link between the internal microstructure of poly(N-isopropylacrylamide)-poly(ethylene glycol) methyl ether methacrylate (PNIPAM-PEGMA) microgels, their bulk moduli and the rheological response and structural arrangement in dense suspensions. The low degree of crosslinking combined with the increased hydrophilicity induced by the presence of PEGMA results in a diffuse, star-like density profile of the particle and very low values of the bulk modulus in dilute conditions, as determined by small angle neutron scattering (SANS). The ultrasoft nature of the particle is reflected in the changes of the structural arrangement in dense suspensions, which evidence a strong deswelling and a sharp rise of the bulk modulus at moderate packing fractions. At larger packings the single particle morphology and softness saturate, and we observe a structural transition from a dispersion-like to a hydrogel-like behavior. The transition is also reflected in the rheological response in the form of a two-step yielding at large packing fractions, characteristic of systems in which a network structure is present. Our results demonstrate that a knowledge of the internal structure and mechanics of individual microgels is needed to determine and tune the properties of dense suspensions, and optimize their response for applications in biomedicine and as filtration systems.