[en] We report ⁷⁵As-NQR/NMR studies on the oxygen-deficient iron (Fe)-based oxypnictide superconductors LaFeAsO_0.6 (T_c=28 K) along with the results on LaFeAsO, LaFeAsO_0.75 (T_c=20 K), and NdFeAsO_0.6 (T_c=53 K). Nuclear spin-lattice relaxation rate 1/T₁ of ⁷⁵As-NQR at zero field on LaFeAsO_0.6 has revealed a T³ dependence below T_c upon cooling without the coherence peak just below T_c, evidencing the unconventional superconducting state with the line-node gap. We have found an intimate relationship between the nuclear quadrupole frequency v_Q of ⁷⁵As and T_c for four samples used in this study. It implies microscopically that the local configuration of Fe and As atoms is significantly related to the T_c of the Fe-oxypnictide superconductors, namely, the T_c can be enhanced up to 50 K when the local configuration of Fe and As atoms is optimal, in which the band structure may be also optimized through the variation of hybridization between As 4 p orbitals and Fe 3d orbitals. (author)