Hyperspectral image super-resolution (HSI-SR) is a crucial research area in remote sensing and precision imaging, aiming to reconstruct high-resolution hyperspectral images (HR-HSI) from low-resolution hyperspectral image (LR-HSI) or multispectral image (MSI) inputs. However, most existing methods are designed for specific input types—such as single HSI input, single MSI input, or their combinations—and lack a unified framework. Consequently, these methods often suffer from limited flexibility and poor generalization when applied to diverse real-world imaging conditions. To address this limitation, we propose OmniNet, a unified HSI-SR framework capable of handling heterogeneous input modalities. OmniNet integrates three specialized sub-networks: the spatial super-resolution network (SpaSR-Net) for single HSI inputs, the spectral super-resolution network (SpeSR-Net) for single MSI inputs, and the fusion super-resolution network (FusionSR-Net) for joint hyperspectral and multispectral image (HSI-MSI) inputs. This cohesive architecture allows for comprehensive modeling of various super-resolution scenarios. Furthermore, we introduce a novel universal dual-domain enhancement module (UDEM) that jointly optimizes spectral and spatial features, significantly enhancing reconstruction performance. Extensive experiments demonstrate that OmniNet consistently outperforms 18 state-of-the-art algorithms across multiple evaluation metrics on two widely used hyperspectral datasets, achieving superior results in both spectral fidelity and spatial clarity.