3D occupancy prediction is gaining traction in autonomous driving for its ability to jointly model environment geometry and semantics. Weakly supervised methods learn 3D representations solely from multi-view 2D labels, making them ideal for data-scarce scenarios. However, distilling 2D knowledge into 3D is challenging due to limited information and noisy pseudo labels. To tackle the above challenges, we introduce MT-Occ, a single-view self-supervised 3D occupancy prediction method that enhances 2D-to-3D distillation by leveraging pretrained multi-task features and modelling task interactions. Our approach includes three effective and flexible components: 1) an effective fusion technique utilising pretrained features of multiple relevant tasks, 2) a spatial cross-task attention module for geometric-semantic distillation and 3) a view-consistent label refinement strategy to improve 2D pseudo labels. MT-Occ achieves state-of-the-art results on autonomous driving benchmarks, outperforming prior work with +16.04% relative mIoU on SSCBench-KITTI-360 and +33.33% on SSCBench-nuScenes, particularly excelling on safety-critical small classes. Extensive experiments validate the effectiveness and flexibility of our design choices.