Multi-task large language models (MTLLMs) are important for many applications at the wireless edge, where users demand specialized models to handle multiple tasks efficiently. However, training MTLLMs is complex and exhaustive, particularly when tasks are subject to change. Recently, the concept of model fusion via task vectors has emerged as an efficient approach for combining fine-tuning parameters to produce an MTLLM. In this paper, the problem of enabling edge users to collaboratively craft such MTLMs via tasks vectors is studied, under the assumption of worst-case adversarial attacks. To this end, first the influence of adversarial noise to multi-task model fusion is investigated and a relationship between the so-called weight disentanglement error and the mean squared error (MSE) is derived. Using hypothesis testing, it is directly shown that the MSE increases interference between task vectors, thereby rendering model fusion ineffective. Then, a novel resilient MTLLM fusion (R-MTLLMF) is proposed, which leverages insights about the LLM architecture and fine-tuning process to safeguard task vector aggregation under adversarial noise by realigning the MTLLM. The proposed R-MTLLMF is then compared for both worst-case and ideal transmission scenarios to study the impact of the wireless channel. Extensive model fusion experiments with vision LLMs demonstrate R-MTLLMF's effectiveness, achieving close-to-baseline performance across eight different tasks in ideal noise scenarios and significantly outperforming unprotected model fusion in worst-case scenarios. The results further advocate for additional physical layer protection for a holistic approach to resilience, from both a wireless and LLM perspective.