Recent years have seen an unprecedented growth in research that leverages the newest computing paradigm of Internet of Drones, comprising a fleet of connected Unmanned Aerial Vehicles (UAVs) used for a wide range of tasks such as monitoring and analytics in highly mobile and changing environments characteristic of disaster regions. Given that the typical data (i.e., videos and images) collected by the fleet of UAVs deployed in such scenarios can be considerably larger than what the onboard computers can process, the UAVs need to offload their data in real-time to the edge and the cloud for further processing. To that end, we present the design of AerialDB - a lightweight decentralized data storage and query system that can store and process time series data on a multi-UAV system comprising: A) a fleet of hundreds of UAVs fitted with onboard computers, and B) ground-based edge servers connected through a cellular link. Leveraging lightweight techniques for content-based replica placement and indexing of shards, AerialDB has been optimized for efficient processing of different possible combinations of typical spatial and temporal queries performed by real-world disaster management applications. Using containerized deployment spanning up to 400 drones and 80 edges, we demonstrate that AerialDB is able to scale efficiently while providing near real-time performance with different realistic workloads. Further, AerialDB comprises a decentralized and locality-aware distributed execution engine which provides graceful degradation of performance upon edge failures with relatively low latency while processing large spatio-temporal data. AerialDB exhibits comparable insertion performance and 100 times improvement in query performance against state-of-the-art baseline. Moreover, it exhibits a 10 times and 100 times improvement with insertion and query workloads respectively over the cloud baseline.