We investigate training machine learning (ML) models across a set of geo-distributed, resource-constrained clusters of devices through unmanned aerial vehicles (UAV) swarms. The presence of time-varying data heterogeneity and computational resource inadequacy among device clusters motivate four key parts of our methodology: (i) stratified UAV swarms of leader, worker, and coordinator UAVs, (ii) hierarchical nested personalized federated learning ( HN-PFL), a distributed ML framework for personalized model training across the worker-leader-core network hierarchy, (iii) cooperative UAV resource pooling to address computational inadequacy of devices by conducting model training among the UAV swarms, and (iv) model/concept drift to model time-varying data distributions. In doing so, we consider both micro (i.e., UAV-level) and macro (i.e., swarm-level) system design. At the micro-level, we propose network-aware HN-PFL, where we distributively orchestrate UAVs inside swarms to optimize energy consumption and ML model performance with performance guarantees. At the macro-level, we focus on swarm trajectory and learning duration design, which we formulate as a sequential decision making problem tackled via deep reinforcement learning. Our simulations demonstrate the improvements achieved by our methodology in terms of ML performance, network resource savings, and swarm trajectory efficiency.