Blind image quality assessment (BIQA) methods often incorporate auxiliary tasks to improve performance. However, existing approaches face limitations due to insufficient integration and a lack of flexible uncertainty estimation, leading to suboptimal performance. To address these challenges, we propose a multitasks-based Deep Evidential Fusion Network (DEFNet) for BIQA, which performs multitask optimization with the assistance of scene and distortion type classification tasks. The framework employs a trustworthy information fusion strategy at two levels: cross sub-region and local-global. The former combines diverse features and patterns across sub-regions, while the latter fuses information from fine- to coarse-grained scales and balances local and global perspectives. Moreover, DEFNet exploits advanced uncertainty estimation technique inspired by evidential learning with the help of normal-inverse gamma distribution mixture. Extensive experiments on both synthetic and authentic distortion datasets demonstrate the effectiveness and robustness of the proposed framework in comparison with state-of-the-art BIQA methods. Additional evaluation and analysis are carried out to highlight its strong generalization capability and adaptability to previously unseen scenarios.