Federated learning (FL) has emerged as a key technique for distributed machine learning (ML). Most literature on FL has focused on ML model training for (i) a single task/model, with (ii) a synchronous scheme for updating model parameters, and (iii) a static data distribution setting across devices, which is often not realistic in practical wireless environments. To address this, we develop DMA-FL considering dynamic FL with multiple downstream tasks/models over an asynchronous model update architecture. We first characterize convergence via introducing scheduling tensors and rectangular functions to capture the impact of system parameters on learning performance. Our analysis sheds light on the joint impact of device training variables (e.g., number of local gradient descent steps), asynchronous scheduling decisions (i.e., when a device trains a task), and dynamic data drifts on the performance of ML training for different tasks. Leveraging these results, we formulate an optimization for jointly configuring resource allocation and device scheduling to strike an efficient trade-off between energy consumption and ML performance. Our solver for the resulting non-convex mixed integer program employs constraint relaxations and successive convex approximations with convergence guarantees. Through numerical experiments, we reveal that DMA-FL substantially improves the performance-efficiency tradeoff.