The way a colloidal glass flows under the influence of external shear is still not fully understood. Here, we study the rheology of glasses of soft thermosensitive core-shell particles with particular emphasis on nonlinear oscillatory and steady measurements and present a comprehensive set of data which display strong nonlinear effects. Step rate experiments exhibit stress overshoots which increase with shear rate, while dynamic strain sweeps reveal a peak in the loss modulus and a yield strain that increases with volume fraction and frequency. Moreover, a Fourier transform analysis of oscillatory measurements yields a significant contribution of high harmonics in the stress which peaks in the shear thinning regime acquiring values up to 25%. A key question is whether shear induced melting is caused by a simple advection process where the shear induced relaxation time, tau, scales inversely proportional with the shear rate, tau proportional to gamma(-1), or is governed by the energy flow in the system, thus depending on both stress, sigma, and shear rate as tau proportional to sigma(-1)gamma(-1). Using a simple phenomenological model based on that of Derec [Phys. Rev. E 67, 061403 (2003)] we managed to reproduce the main features of our rheological data, the shape of the stress oscillations in the dynamic measurements, as well as the strain dependence of the higher harmonic contribution. This analysis suggests that nonlinearities are important during the yielding process, and the shear induced relaxation time follows a nontrivial dependence on both the stress and strain rate.