The fundamental understanding of the microscopic origin of oxygen diffusion is essential to design and optimize new oxygen ion conductors for technological applications. In this work, using single crystal neutron diffraction studies on Sr and O-doped Nd2NiO4+δ compounds, we have shown strong anharmonic delocalization of apical oxygen atoms specifically towards the nearest oxygen interstitial sites which are related to specific low energy local structural distortions induced by the excess oxygens. These structural distortions are prerequisites to trigger oxygen mobility close to room temperature. The subsequent oxygen diffusion mechanism is closely related to the “phonon assisted diffusion mechanism” providing an atomistic description of non-classical oxygen diffusion process in non-stoichiometric oxides at low temperature. A commensurate antiferromagnetic spin order is observed in Nd2NiO4.1 in contrast to an incommensurate magnetic order in Nd2NiO4.23. The observed incommensurate magnetic phase is different from the usual stripe type magnetic order observed in isoelectronic Sr-doped Nd1.5Sr0.5NiO4+δ compound.