Forecasting problems of integrated energy systems include: a lack of models for multi-energy coupling relations; poor collection of multi-scale temporal features; insufficient long-term dependency modeling and non-linear adaptive mapping capabilities. Given the problems mentioned above, this paper proposes the Omni-Energy framework, which consists of a 3D-CNN tensor reconstruction module, a multi-scale 2D-CNN with parallel convolutional kernels, a ViT-KAN module for adaptive nonlinear dependency modelling, and a SENet attention mechanism to dynamically weigh external factors. Four sets of real-world data are used for all-around verification: HEEW (147 buildings), a chemical industrial park in Northern China, the Bangladesh PGCB dataset with load shedding events, and the San Diego dataset with high renewable penetration. Based on experimental results, Omni-Energy has shown considerable improvements over the 12 best existing methods for reducing the RMSE of electricity, heat and cooling load prediction by 18.7%, 22.3% and 19.8% respectively on the HEEW dataset. Based on the ablation study, all the modules are necessary, and the KAN component improves the stability of prediction by over 35% in difficult situations, such as bad weather and holidays.