The nonlocal nature of the polaron formation in t - t '- t'' - J model is studied in large lattices up to 64 sites by developing a new numerical method. We show that the effect of longer-range hoppings t' and t'' is a large anisotropy of the electron-phonon interaction (EPI) leading to a completely different influence of EPI on the nodal and antinodal points in agreement with the experiments. Furthermore, nonlocal EPI preserves polaron's quantum motion, which destroys the antiferromagnetic order effectively, even in the strong coupling regime, although the quasiparticle weight in angle-resolved-photoemission spectroscopy is strongly suppressed.