We have investigated the role of oxygen stoichiometry and structural properties in the modulation of Co valence and spin state in single-layer La(2-x)A(x)CoO(4 +/-delta) (A = Sr, Ca; 0 <= x <= 1) perovskites as well as the interplay between their local structural properties and the magnetic and charge-ordering phenomena. We show the results of high angular resolution powder X-ray diffraction and Co K-edge X-ray absorption and emission spectroscopy experiments on polycrystalline and single-crystal samples. The different doping-induced changes in the Co valence and spin state by Ca (or Sr) substitution can be understood in terms of the evolving oxygen stoichiometry. For Ca doping, the interstitial oxygen excess around the La/Ca atoms in underdoped samples is rapidly lost upon increasing the Ca content. The creation of oxygen vacancies leads to the stabilization of a mixed-valence Co2.5+ independently of the Ca content. In contrast, Sr substitution leads to almost stoichiometric samples and a lower oxygen vacancy concentration, which allows higher mixed-valence states for Co up to Co2.9+. The Co mixed-valence state along the two series is fluctuating between two valence states, Co2.4+ as in La2CoO4.2 and Co2.9+ as in LaSrCoO3.91, that become periodically ordered for the charge-ordered phases around the half-doping. The X-ray emission derived spin states agree well with the Co fluctuating mixed-valence state derived from X-ray absorption spectroscopy on consideration of a distribution of high-spin Co2+ and low-spin Co3+. Furthermore, there is no quenching of the orbital contribution for the high-spin Co2+, as concluded from a comparison with macroscopic magnetization measurements. Doping holes are mainly located in the ab plane and have a strong oxygen 2p character. The major lattice distortions, which are different for Sr and Ca doping, occur along the c axis, where changes in the oxygen stoichiometry take place. Moreover, charge-order transitions are clearly shown from the anomalous increase of the c lattice parameter with an increase in the temperature above 500 K but there is no signature for a temperature-dependent spin-state transition.