Nonlinear vortex gyrotropic motion in a three-nanocontacts system is investigated by micromagnetic simulations and analytical calculations. Three out-of-plane spin-polarized currents are injected into a nanodisk through a centered nanocontact and two off-centered nanocontacts, respectively. For current combination (ip1, ip0, ip2)=(?1,1,?1), the trajectory of the vortex core is a peanut-like orbit, but it is an elliptical orbit for (ip1, ip0, ip2)=(1, 1,?1). Moreover, the gyrotropic frequency displays peaks for both current combinations. Analytical calculations based on the Thiele equation show that the changes of frequency can be ascribed mainly to the forces generated by the Oersted field accompanying the currents. We also demonstrate a dependence of eigenfrequency shifts on the direction and distance of the applied currents.