Magnetic and zero-field nuclear magnetic resonance investigations have been made on the La2-xSrCoO4 system (x=0-1.4), one of the isomorphous compounds of the superconducting cuprates. In the La-rich region (x less-than-or-equal-to 0.5), the antiferromagnetic (AF) ordering persists and the internal magnetic field at 1.4 K remains almost constant (H(int)(Co) congruent-to 200 kOe), though the Neel temperature shows an initial strong decrease with a small amount of Sr substitution. When x increases further (x greater-than-or-equal-to 0.6), the AF state suddenly transforms to a ferromagnetic state and the Curie temperature shows a maximum (T(C)=220 K) at x=0.9. Spontaneous magnetizations at T=4.2 K are, however, non-zero (2.2-1.6 mu(B)) only in the range of x=0.7-0.9, and H(int)(Co) strongly decreases from 190 kOe (x=0.6) to below 40 kOe (x=1.1). Co-59 spin-lattice relaxation time T1 for x=0.7 and 0.9 follows the relation T1T=const., suggesting it is in a metallic state.