Multimodal fake news detection plays a crucial role in combating online misinformation. The inherent domain diversity of news in the real world has driven the development of cross-domain detection methods. However, these detection methods either suffer from significant performance degradation due to semantic and deception pattern shifts between the training (source) and test (target) domains or heavily rely on annotated labels. To address the problems, we propose ADOSE, an active multi-source domain adaptation framework for multimodal fake news detection which actively annotates a small subset of target samples to improve detection performance. Specifically, for domain shifts, we design a multi-expert classifier network based on refined features to comprehensively capture and adapt to the semantic space and deception patterns of news across different domains. To maximize adaptation performance with limited annotation cost, we propose a least-disagree uncertainty selector equipped with a diversity calculator for selecting the most informative samples. The selector leverages the uncertainty of inconsistent predictions before and after perturbations by multiple classifiers as an indicator of unfamiliar samples. It further incorporates diversity scores derived from multi-view features to ensure the chosen samples achieve maximal coverage of target domain features. The extensive experiments on multiple datasets show that ADOSE outperforms existing domain adaptation methods by 2.45\% $\sim$ 9.1\%, indicating the superiority of our model.