139La zero-field NMR measurements and NMR measurements under external magnetic fields in the layered perovskite compound La2-xSrxNiO4 (x=0-1.3) have been carried out at low temperatures. With the Sr substitution three different 139La resonances were observed as follows. In the antiferromagnetic (AF) state for 0<or=x<or=1.0, (i) zero-field NMR with a large internal magnetic field of approximately 18 kOe, whose intensity decreases linearly with x up to x=1.0 and (ii) NMR With K approximately O Knight shift and broad line-width ( approximately 4 kOe for x=0.9), whose intensity increases rapidly in the region close to x=1.0. In the regions close to x approximately 0 and to x approximately 1.0, the relaxation rate T1-1 of 139La zero-field NMR and NMR Under an external field is proportional to T2.6 and to Tapproximately 2.7, respectively, corresponding to the 3D long-range order of antiferromagnetism (LOAF). In the paramagnetic state for x>1.0, (iii) NMR With K approximately 0 but rather sharp line-width ( approximately 2 kOe for x=1.3). T1-1 follows a Koninga-like relation, T1T=constant, indicating a metallic state. We concluded that in the insulative AF region (0<or=x<or=1.0) the doped holes occupy mainly the Ni 3d(z2) orbital and, with increasing x, the LOAF state at x approximately 0 associated with Ni2+ (S= 1/2 ) spins translates to the LOAF state at x approximately 1.0 with Ni3+ (S= 1/2 ) spins. On further substitution of Sr above x>or approximately=1.0, the excess holes should go into the O 2px,y orbital in the Ni-O plane through the Ni 3d(x2-y2) orbital. Giving rise to the spin frustration of the Ni3+ (S= 1/2 ) spins.