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Federated multi-task learning (FMTL) is a promising edge learning framework to fit the data with non-independent and non-identical distribution (non-i.i.d.) by leveraging the statistical correlations among the personalized models. For many practical applications in wireless communications, the sensory data are not only heterogeneous but also non-stationary due to the mobility of terminals and the randomness of link connections. The non-stationary heterogeneous data may lead to model divergence and staleness in the training stage and poor test accuracy in the inference stage. In this paper, we shall develop an adaptive FMTL framework, which works well with non-stationary data. We further propose to optimize the model updating and cluster splitting schemes in the training stage to accelerate model convergence. We also design low-complexity model selection schemes and pruning schemes in both the training and inference stages to select the best model for fitting the current data and delete redundant models, respectively. The proposed framework is validated in the edge learning model, namely, the linear regression problem for wireless indoor localization and graph neural network for wireless power control. Experimental results demonstrate that the proposed framework can accelerate the model training convergence and reduce the computation complexity while ensuring model accuracy.