We analyze the stability of Neel and collinear orders for the frustrated J1-J2 model on a square lattice as a function of S and J2/J1 within the Schwinger-boson mean-field theory. For Neel order and finite S, the domain of stability extends beyond the classical boundary J2/J1 = 1/2, suggesting the possibility of stabilizing (with the help of quantum fluctuations) a state that is classically forbidden. We use the solution with short-range Neel order as an effective model for the magnetic properties of high-T(c) Cu oxides. Predictions are made for the static susceptibility, the dynamical structure factor, and the nuclear relaxation rates (all observable experimentally) at all temperatures. We show that the spin waves are overdamped even at low T and that a gap opens in the spin-fluctuation spectrum. The susceptibility is nearly linear on a wide intermediate temperature range and obeys a Curie law at high temperature in agreement with 1/N fermionic expansion.