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Multi-Task Learning (MTL) is widely used in automatic stuttering detection to identify stuttering symptoms; however, task conflicts can hinder performance. This paper addresses the task conflict issue in MTL-based stuttering detection and proposes a rule-based MTL strategy and a Multi-Mixture-of-Experts (MMoE) MTL framework to alleviate these conflicts. We analyze the inherent conflicts in stuttering detection tasks and develop a rule-based MTL strategy to mitigate them. Additionally, we introduce an MoE-based adaptive multi-task strategy to optimize task allocation. Experimental results show that our approach outperforms current state-of-the-art methods. In the 2024 SLT Stuttering Speech Challenge, the rule-based MTL strategy achieved a 19.9% increase in average F1 score over the baseline, securing first place. The MMoE-MTL strategy further enhanced task collaboration, improving the average F1 score by 7.55%, demonstrating its effectiveness.