We perform immersed-boundary-method numerical simulations of oscillatory shear flow of suspensions of mono-disperse non-colloidal rigid spherical particles in a Newtonian liquid from the dilute to the concentrated regime. Both small and large amplitude oscillatory shear flow (SAOS and LAOS, respectively) are studied and the effects of particle concentration, fluid inertia, particle-to-fluid density ratio, and deformation amplitude on the measured apparent viscoelastic moduli of the suspensions are quantified. In the SAOS regime, a non-zero storage modulus G '-values significantly change with inertia, but depend on the volume fraction of the solid phase only for suspensions of particles denser than the fluid. On the other hand, the loss modulus G '' increases with both inertia and particle concentration. In the LAOS regime, the moduli are only weakly dependent on the deformation amplitude for a dilute suspension, whereas non-monotonic variations are observed at high concentrations.