High-pressure synthesized quasi-one-dimensional NaMn₂O₄ and Li_0.92Mn₂O₄ are both antiferromagnetic insulators. Here their atomic and magnetic structures are investigated using neutron powder diffraction. The present crystal structural analyses of NaMn₂O₄ reveal that a Mn³⁺/Mn⁴⁺ charge-ordering state exists even at low temperature (down to 1.5 K). It is evident that one of the Mn sites shows a strongly distorted Mn³⁺ octahedron due to the Jahn-Teller effect. Above T_N = 35 K, a two-dimensional short-range correlation is observed, as indicated by asymmetric diffuse scattering. Below T_N, two antiferromagnetic transitions are observed: (i) a commensurate long-range Mn³⁺ spin ordering below T_N1 = 35 K and (ii) an incommensurate Mn⁴⁺ spin ordering below T_N2 = 11 K. Surprisingly, the two antiferromagnetic orders are found to be independent of each other. The commensurate magnetic structure (k_C = 0.5, 0.5, 0.5) follows the magnetic anisotropy of the local easy axes of Mn³⁺, while the incommensurate Mn⁴⁺ one shows a spin-density-wave or a cycloidal order with k_IC = (0,0, 0.216). For Li_0.92Mn₂O₄, on the other hand, the absence of a long-range spin-ordered state is confirmed down to 1.5 K.