We have investigated the generation of spin waves in the free layer of an extended spin-valve structure with a nanoscaled point contact driven by both microwave and direct electric current using Brillouin light scattering microscopy. Simultaneously with the directly excited spin waves, strong nonlinear effects are observed, namely, the generation of eigenmodes with integer multiple frequencies (2f, 3f, 4f) and modes with noninteger factors (0.5f, 1.5f) with respect to the excitation frequency f. The origin of these nonlinear modes is traced back to three-magnon-scattering processes. The direct current influence on the generation of the fundamental mode at frequency f is related to the spin-transfer torque, while the efficiency of three-magnon-scattering processes is controlled by the Oersted field as an additional effect of the direct current.