The J1-J2 square lattice Heisenberg model with spin S=1/2 has three phases with long-range magnetic order and two unconventionally ordered phases depending on the ratio of exchange constants. It describes a number of recently found layered vanadium oxide compounds. A simple means of investigating the ground state is the study of the magnetization curve and high-field susceptibility. We discuss these quantities by using the spin-wave theory and the exact diagonalization in the whole J1-J2 plane. We compare both results and find good overall agreement in the sectors of the phase diagram with magnetic order. Close to the disordered regions the magnetization curve shows strong deviations from the classical linear behaviour caused by large quantum fluctuations and spin-wave approximation breaks down. On the FM side (J1<0) where one approaches the quantum gapless spin nematic ground state this region is surprisingly large. We find that inclusion of second order spin-wave corrections does not lead to fundamental improvement. Quantum corrections to the tilting angle of the ordered moments are also calculated. They may have both signs, contrary to the always negative first order quantum corrections to the magnetization. Finally we investigate the effect of the interlayer coupling and find that the quasi-2D picture remains valid up to |J_\perp/J1| ~ 0.3.