Optical and Synthetic Aperture Radar (SAR) imagery provides complementary resources for land cover classification via spectral richness and all-weather sensing. Despite their potential, integrating these modalities remains challenging due to significant disparities in spatial resolution, imaging physics, and the inherent speckle noise in SAR data. Existing fusion frameworks often employ homogeneous feature extraction strategies that fail to account for these heterogeneous characteristics, leading to insufficient information integration and blurred semantic boundaries. To address these issues, we propose a Cross-Resolution dual-branch multi-task Fusion Network (CRFNet). The methodology features an asymmetric encoding architecture that utilises ResNet for high-resolution optical data and a Swin Transformer equipped with an Attention-Guided SAR Enhancement (AGSE) block for SAR data. Furthermore, a Modal-aware Adaptive Fusion Module (MAFM) is introduced to dynamically modulate feature injection, while a Multi-Scale Context Aggregation (MSCA) module facilitates deep feature enhancement. CRFNet achieves the highest overall performance among the compared methods, with an Overall Accuracy (OA), mean Intersection over Union (mIoU), and Mean F1-Score (M-F1) of 86.42%, 76.07%, and 81.48%, respectively, on the Shandong dataset, and 71.86%, 55.43%, and 66.28%, respectively, on the Jiangsu dataset. Cross-region tests without target-region fine-tuning, CRFNet obtains mIoU values of 49.32% (Shandong-to-Jiangsu) and 63.05% (Jiangsu-to-Shandong).