Debris disks are signposts of analogues to small body populations of the Solar System, often however with much higher masses and dust production rates. The disk associated with the nearby star Eta Corvi is especially striking as it shows strong mid- and far-infrared excesses despite an age of ~1.4 Gyr. We undertake to construct a consistent model of the system able to explain a diverse collection of spatial and spectral data. We analyze Keck Interferometer Nuller measurements and revisit Spitzer and additional spectro-photometric data, as well as resolved Herschel images to determine the dust spatial distribution in the inner exozodi and in the outer belt. We model in detail the two-component disk and the dust properties from the sub-AU scale to the outermost regions by fitting simultaneously all measurements against a large parameter space. The properties of the cold belt are consistent with a collisional cascade in a reservoir of ice-free planetesimals at 133 AU. It shows marginal evidence for asymmetries along the major axis. KIN enables us to establish that the warm dust consists in a ring that peaks between 0.2 and 0.8 AU. To reconcile this location with the ~400 K dust temperature, very high albedo dust must be invoked and a distribution of forsterite grains starting from micron sizes satisfies this criterion while providing an excellent fit to the spectrum. We discuss additional constraints from the LBTI and near-infrared spectra, and we present predictions of what JWST can unveil about this unusual object and whether it can detect unseen planets.