Oxygen interstitials and vacancies play a key role in modulating the microstructure and properties of nonstoichiometric oxide systems, such as those used for superconductors and multiferroics. Key to understanding the tuning mechanisms resulting from oxygen doping is a knowledge of the precise positions of these lattice defects, and of the interaction both between these defects and with many order parameters. Here, we report how such information can, for the first time, be obtained from a sample of LuFe_{2}O_{4.22} using a range of techniques including advanced electron microscopy, atomic-resolution spectroscopy, and density functional theory calculations. The results provide quantitative atomic details of the crystal unit cell, together with a description of the ferroelastic, ferroelectric, and ferromagnetic order parameters. We elucidate also the interaction between these order parameters and the positions of the oxygen interstitials in the oxygen-enriched sample. The comprehensive analysis of oxygen interstitial ordering provides insights into understanding the coupling among different degrees of freedom in rare earth ferrites and demonstrates that oxygen content regulation is a powerful tool for tuning the microstructure and properties for this class of quantum material.