This paper proposes a low-power online anomaly detection framework based on neuromorphic wireless sensor networks, encompassing possible use cases such as brain-machine interfaces and remote environmental monitoring. In the considered system, a central reader node actively queries a subset of neuromorphic sensor nodes (neuro-SNs) at each time frame. The neuromorphic sensors are event-driven, producing spikes in correspondence to relevant changes in the monitored system. The queried neuro-SNs respond to the reader with impulse radio (IR) transmissions that directly encode the sensed local events. The reader processes these event-driven signals to determine whether the monitored environment is in a normal or anomalous state, while rigorously controlling the false discovery rate (FDR) of detections below a predefined threshold. The proposed approach employs an online hypothesis testing method with e-values to maintain FDR control without requiring knowledge of the anomaly rate, and it dynamically optimizes the sensor querying strategy by casting it as a best-arm identification problem in a multi-armed bandit framework. Extensive performance evaluation demonstrates that the proposed method can reliably detect anomalies under stringent FDR requirements, while efficiently scheduling sensor communications and achieving low detection latency.