The increasing adoption of UAVs equipped with advanced sensors and GPU-accelerated edge computing has enabled real-time AI-driven applications in domains such as precision agriculture, wildfire monitoring, and environmental conservation. However, the integrated design and orchestration of navigation, sensing, and analytics, together with seamless real-time coordination across drone, edge, and cloud resources, remains a significant challenge. To address these challenges, we propose AeroDaaS, a service-oriented framework that abstracts UAV-based sensing complexities and provides a Drone-as-a-Service (DaaS) model for intelligent decision-making. AeroDaaS offers modular service primitives for on-demand UAV sensing, navigation and analytics as composable microservices, ensuring cross-platform compatibility and scalability across heterogeneous UAV and edge-cloud infrastructures. AeroDaaS also supports plug-and-play scheduling modules, including Waypoint and Analytics schedulers, which enable trajectory optimization and real-time coordination of inference workloads. We implement and evaluate AeroDaaS for six real-world DaaS applications, of which two are evaluated in real-world scenarios and four in simulation. AeroDaaS requires less than 40 lines of code for the applications and has minimal platform overhead of less than 20 ms per frame and about 1 GB memory usage on Orin Nano and a AMD RTX 3090 GPU workstation. These results are promising for AeroDaaS as an efficient, flexible and scalable UAV programming framework for autonomous aerial analytics.