The brain performs cognitive functions through rhythmic communications of neural oscillations across numerous spatially distributed neurons. This process is known as "binding by synchrony". Herein, we demonstrate oscillatory neural networks (ONNs) based on a nanoscale NbOx device for compact oscillation neurons (ONs). When a voltage (V-DD) is applied to the NbOx-based device, a high resistance state is temporarily changed to a low resistance state due to the formation of a conducting path. Owing to the volatile switching characteristics, the VDD across the NbOx device, serially connected with an additional load resistor (R-L), is repeatedly increased and decreased, generating oscillations at the intermediate node. We experimentally investigated the impact of R-L and V-DD on the oscillation behavior of the single ON circuit. Thereafter, through simulations, we analyzed the interactions between the voltage oscillations when two NbOx-based ONs were connected by a coupling element (e.g., variable resistor or capacitor). The results showed that the oscillations were either in- or out-of-phase synchronized owing to the coupling strength. These two distinguishable synchronizations can be used to encode binary information in the phase domain, resulting in energy-efficient computing. This study proves that by building ONNs comprising multiple ONs, both sharp edges and pretrained patterns can be detected from images.