We report on the structural properties of the La-4(Co1-xNix)(3)O-10 solid solution at and above room temperature based on synchrotron powder diffraction data. The monoclinic P2(1)/a structure at ambient conditions transforms via an orthorhombic intermediate to a high temperature I4/mmm tetragonal phase. Significant anisotropic strain causes peak broadening for some Bragg reflections of the monoclinic and orthorhombic phases. Smaller intensity deviations for the tetragonal structure are possibly caused by minor amounts (< 1%) of stacking faults along [001]. La4Co3O10 shows oxygen hyperstoichiometry in air, however, in N-2 the oxygen stoichiometry is close to 10.00 for all x. Atomistic simulations were performed to evaluate total energies for potential polymorphs; and to calculate energies of formation of oxygen defects in terms of vacancies at apical O-sites towards the rock salt (RS) like layer, and within the perovskite blocks, in addition to interstitial oxygen atoms in the rock salt layers. cNEB simulations were performed for predicting energy barriers for mobility along various diffusion pathways. The barrier is lowest for tetragonal phase. Consistent with reports on La2CoO4 and La2NiO4 also the RP3 phase appears to have interstitial oxygen transport as the governing migration mechanism with a barrier height of around 0.40 eV.