A key challenge in the development of inorganic-organic nanocomposites is the mechanical behavior identification of the organic phase. For supercrystalline materials, in which the organic phase ranges down to sub-nm areas, the identification of the organic materials' mechanical properties is however experimentally inaccessible. The supercrystalline nanocomposites investigated here are 3D superlattices of self-assembled iron oxide nanoparticles, surface-functionalized with crosslinked oleic acid ligands. They exhibit the highest reported values of Young's modulus, nanohardness and strength for inorganic-organic nanocomposites. A multiscale numerical modeling approach is developed to identify these properties using supercrystalline representative volume elements, in which the nanoparticles are arranged in a face-centered cubic superlattice and the organic phase is modeled as a thin layer interfacing each particle. A Drucker-Prager-type elastoplastic constitutive law with perfectly plastic yielding is identified as being able to describe the supercrystals' response in nanoindentation accurately. As the nanoparticles behave in a purely elastic manner with very high stiffness, the underlying constitutive law of the organic phase is also identified to be Drucker-Prager-type elastoplastic, with a Young's modulus of 13GPa and a uniaxial tensile yield stress of 900 MPa, remarkably high values for an organic material, and matching well with experimental and DFT-based estimations. Furthermore, a sensitivity study indicates that small configurational changes within the supercrystalline lattice do not significantly alter the overall stiffness behavior. Multiscale numerical modeling is thus proven to be able to identify the nanomechanical properties of supercrystals, and can ultimately be used to tailor these materials' mechanical behavior starting from superlattice considerations.