Charge ordering phenomena and their effects on charge dynamics have been investigated for single crystals of R2-xSrxNiO4 (R = La, Nd) with x = 0.5 for R = La and 0.33less than or equal toxless than or equal to0.70 for R = Nd by measurements of neutron diffraction and optical reflectivity spectra. The essential features of charge dynamics for 0.33less than or equal toxless than or equal to0.5 appear to be least affected by R species (La or Nd). In xgreater than or equal to0.5, commensurate checkerboard (CB)-type charge order shows up at such a high temperature as T(CO)(C)similar to480 K. An incommensurate stripe order, that tends to take over the CB-type charge order at lower temperatures, is also clearly observed up to x = 0.7. The remarkable evolution of the pseudogap feature as lowering temperature is observed in the optical conductivity spectrum. As x is increased, the energy scale (Delta(PG)), the onset T (T-PG) of the pseudogap, and the in-plane resistivity upturn T (T-rhoab) scale with each other and decrease monotonically after taking a maximum at x = 0.5, as T-CO(C) is simultaneously reduced. The results indicate that the charge dynamics is significantly regulated by emergence of the CB-type charge correlation, and that the melting of the CB-type charge order must be playing a key role in driving the insulator-metal transition at xsimilar to0.9.