We report a comprehensive La139 and Cu63 nuclear magnetic resonance study on La2-xSrxCuO4 (0.07≤x≤0.2) single crystals. The La139 spin-lattice relaxation rate T1-1139 is drastically influenced by Sr doping x at low temperatures. A detailed field dependence of T1-1139 at x=1/8 suggests that charge ordering induces the critical slowing down of spin fluctuations toward glassy spin order and competes with superconductivity. On the other hand, the Cu63 relaxation rate T1-163 is well described by a Curie-Weiss law at high temperatures, yielding the Curie-Weiss temperature Θ as a function of doping. Θ changes sharply through a critical hole concentration xc∼0.09. xc appears to correspond to the delocalization limit of doped holes, above which the bulk nature of superconductivity is established.