Multi-task learning is an effective way to address the challenge of model personalization caused by high data heterogeneity in federated learning. However, extending multi-task learning to the online decentralized federated learning setting is yet to be explored. The online decentralized federated learning setting considers many real-world applications of federated learning, such as autonomous systems, where clients communicate peer-to-peer and the data distribution of each client is time-varying. A more serious problem in real-world applications of federated learning is the presence of Byzantine clients. Byzantine-resilient approaches used in federated learning work only when the number of Byzantine clients is less than one-half the total number of clients. Yet, it is difficult to put a limit on the number of Byzantine clients within a system in reality. However, recent work in robotics shows that it is possible to exploit cyber-physical properties of a system to predict clients' behavior and assign a trust probability to received signals. This can help to achieve resiliency in the presence of a dominating number of Byzantine clients. Therefore, in this paper, we develop an online decentralized federated multi-task learning algorithm to provide model personalization and resiliency when the number of Byzantine clients dominates the number of honest clients. Our proposed algorithm leverages cyber-physical properties, such as the received signal strength in wireless systems or side information, to assign a trust probability to local models received from neighbors in each iteration. Our simulation results show that the proposed algorithm performs close to a Byzantine-free setting.