Many-body potentials up to fourth order are constructed using nonrelativistic, scalar-relativistic, and relativistic coupled-cluster theory to accurately describe the interaction between superheavy oganesson atoms. The obtained distance-dependent energy values were fitted to extended two-body Lennard-Jones and three-body Axilrod-Teller-Muto potentials, with the fourth-order term treated through a classical long-range Drude dipole interaction model. From these interaction potentials, spectroscopic constants for the oganesson dimer and solid-state properties were obtained. Furthermore, these high-level results are compared to scalar-relativistic and two-component plane-wave DFT calculations based on a tailor-made projector augmented wave pseudopotential (PAW-PP) and newly derived parameters for Grimme's dispersion correction. It is shown that the functionals PBE-D3(BJ), PBEso1, and in particular SCAN provide excellent agreement with the many-body reference for solid oganesson. Finally, the results for oganesson are compared and related to the lighter rare gas elements, and periodic trends are discussed.