Abstract: Real-time decoding of omnidirectional images is essential for immersive virtual reality (VR) experiences. Compared with conventional transform-based learned image compression (LIC), overfitted codecs offer lower decoding complexity by representing each image with a lightweight implicit neural representation (INR). However, existing approaches typically operate on the equirectangular projection (ERP), which introduces nonuniform spherical sampling and spatial distortion, leading to redundant sampling near the poles and latitude-dependent receptive fields. To address these limitations, we propose a spherical overfitted codec based on a multi-scale Hierarchical Equal Area isoLatitude Pixelization (HEALPix) representation, which enables equal-area sampling and efficient hierarchical modeling of spherical signals. Building on this representation, we develop a Spherical Inter-Scale Conditional entropy model that exploits spatial dependencies and cross-scale correlations among HEALPix latents to improve coding efficiency. We further introduce a Multi-Ring Spherical Convolution that aggregates neighboring pixels over a nearly uniform spherical receptive field across latitudes. Experiments on a public omnidirectional image dataset demonstrate BD-rate reductions of 16.3%, 26.5%, and 19.5% over VVC in terms of V-PSNR, V-MS-SSIM, and V-LPIPS, respectively. Our method also achieves a 13.1% BD-rate reduction over ERP-based Cool-Chic 5.0 in terms of V-PSNR, while providing 2.6-3.6x faster decoding than the evaluated learned autoencoder codecs.