Ln[subscript]2CuO[subscript]4 (Ln = La, Pr, Nd, Sm, Eu, Gd) undergo structural transitions to oxygen-reduced structures Ln[subscript]2CuO[subscript]4-d with Ln = La, d = 1/3 and Ln = Pr, Nd, Sm, Eu, Gd, d = 1/2. The Nd[subscript]2CuO[subscript]4-type (T[superscript]'-phase) La[subscript]2CuO[subscript]4+d is observed after reoxygenation of oxygen-reduced La[subscript]2CuO[subscript]3.67 structure below 500°C. The magnetic properties of T/O (K[subscript]2NiF[subscript]4-type structure)-phase La[subscript]2CuO[subscript]4 systems show quite different behaviors compared with those of conventional solid state reacted La[subscript]2CuO[subscript]4 systems. The implications of these nonsuperconducting behaviors within the superconducting carrier concentrations are discussed from the structural point of view;La[subscript]2-xM[subscript]xCuO[subscript]4+d (M = Ca, Sr; x = 0.05, 0.15), synthesized by the low temperature route, also contain excess oxygen and show different physical properties. [superscript]139La NQR measurements of nonsuperconducting La[subscript]1.85Sr[subscript]0.15CuO[subscript]4.04 show metallic properties. The tolerance factor, which is based on ionic radii, is quite successful to describe structural properties of K[subscript]2NiF[subscript]4 related cuprate compounds. With anisotropic thermal motions of apical oxygens in La[subscript]2CuO[subscript]4, we discuss the crucial role of out-of-plane oxygens for stabilization of cuprate structures;The magnetic phase diagram and phase separation of La[subscript]2-xSr[subscript]xCuO[subscript]4+[delta] system (0.000≤ x≤ 0.030, 0.0≤[delta]) are reported. From the decrease of T[subscript]c by doping level, we infer the localization and pair-breaking mechanism induced by doped holes. Phase separation is realized within the appearance of three-dimensional antiferromagnetic order. We also observe scaling properties of susceptibilities versus renormalized temperatures and infer the finite size effects by doped holes from the scaling;[superscript]139La NQR spin-lattice relaxation rates vs temperature are presented for La[subscript]2-xSr[subscript]xCuO[subscript]4 with x = 0.02 to 0.08. The spin-lattice relaxation rate below ~2T[subscript]N(x) shows a power-law critical behavior while above ~2T[subscript]N(x) it follows an exponential law with a small x-dependent spin-stiffness constant, where T[subscript]N is the magnetic ordering temperature. It is argued that the spin-lattice relaxation rate arises from fluctuations of the staggered magnetization in locally ordered mesoscopic domains. We infer that the magnetically ordered state is not a conventional spin glass.