The dynamical and rheological properties of ultrasoft colloids and star polymers are investigated in dilute and semidilute solutions under linear shear flow. We apply a hybrid mesoscale hydrodynamics simulation approach, which combines molecular dynamics simulations for the solute with the multiparticle collision dynamics approach for the solvent. We investigate the effect of concentration on relaxation, diffusion, and the rheological properties of the star polymers. We find that the relaxation time of a star-polymer arm is a universal function of a concentration-dependent Weissenberg number. The center-of-mass mean square displacements of the star polymers are anisotropic under shear flow. At high shear rate, we find shear-induced enhanced center-of-mass displacements along the vorticity and gradient directions. Moreover, we determine the shear viscosity and normal stress coefficients as a function of concentration. The shear viscosity exhibits shear thinning with a weak functionality dependence.