$360^{\circ}$ omnidirectional images (ODIs) have gained considerable attention recently, and are widely used in various virtual reality (VR) and augmented reality (AR) applications. However, capturing such images is expensive and requires specialized equipment, making ODI synthesis increasingly important. While common 2D image generation and editing methods are rapidly advancing, these models struggle to deliver satisfactory results when generating or editing ODIs due to the unique format and broad 360$^{\circ}$ Field-of-View (FoV) of ODIs. To bridge this gap, we construct \textbf{\textit{Any2Omni}}, the first comprehensive ODI generation-editing dataset comprises 60,000+ training data covering diverse input conditions and up to 9 ODI generation and editing tasks. Built upon Any2Omni, we propose an \textbf{\underline{Omni}} model for \textbf{\underline{Omni}}-directional image generation and editing (\textbf{\textit{Omni$^2$}}), with the capability of handling various ODI generation and editing tasks under diverse input conditions using one model. Extensive experiments demonstrate the superiority and effectiveness of the proposed Omni$^2$ model for both the ODI generation and editing tasks. Both the Any2Omni dataset and the Omni$^2$ model are publicly available at: https://github.com/IntMeGroup/Omni2.