We have investigated magnetic excitations in both the stripe (x < 0.5) and overdoped checkerboard (CB) (x ≥ 0.5) regions in Nd2-xSrxNiO4 (x = 0.33, 0.60, and 0.70) samples by inelastic neutron scattering. The magnetic excitations of Nd1.67Sr0.33NiO4 in the stripe region can be described by the linear spin wave theory with the same exchange constants as estimated for La5/3Sr1/3NiO4. In strong contrast to the well-defined spin wave excitations in the stripe region, the CBordered x = 0.60 and 0.70 samples show nondispersive broad magnetic excitation spectra. The broad feature of the excitation spectra in the CB region appears to be independent of the hole concentration up to x = 0.7. We discuss the origin of the broad excitation spectra and the robustness of the CB order above x > 0.5.