We investigate the orientation transition and strain relaxation in oxygenated epitaxial strontium-doped lanthanum nickelate, La1.875Sr0.125NiO4+δ (LSNO) thin films grown on single crystal strontium titanate, SrTiO3 (STO) substrates. Structural evolution has been studied as a function of film thickness by x-ray diffraction, pole figure analysis, and transmission electron microscopy (TEM). The LSNO layer grows epitaxial (OR1) with respect to the STO substrate with an orientation (001)OR1//(001)STO and <001>OR1//<001>STO. This orientation is maintained up to approximately 15 nm as observed from TEM, at which point it undergoes reorientation and lattice mismatch strain relaxation. The growth continues with a new orientation (OR2) as (100)OR2//(001)OR1 and with <100>OR2//<001>OR1 and <001>OR2//<001>OR1 with respect to the epitaxial LSNO layer. We consider possible mechanisms in detail leading to these phenomena given that the potassium nickel fluoride (K2NiF4)-structured lattice is able to accommodate excess oxygen interstitials and corresponding changes in the Ni valence state. By investigating the phase space of deposition parameters, we experimentally identify key factors leading to the reorientation phenomena.