In this paper, we assess an innovative concept of emulating biological neurons with oscillators to implement an oscillatory neural network (ONN) with beyond-CMOS devices based on vanadium dioxide (VO2). ONNs can be of interest as an ultra-low-power neuromorphic architecture capable of performing associative memory tasks, such as pattern recognition in IoT edge devices. To explore the benefits and costs of beyond-CMOS ONNs necessitates modeling, simulation, and design methods spanning from materials (e.g., atomistic methods) to devices (e.g., technology-computer-aided-design, TCAD) up to circuits (e.g., mixed-mode simulation, compact modeling). In this work, we report on the development of such an advanced design toolbox and the results on performance and features of beyond-CMOS ONNs. The proposed design toolbox allows exploring ONN scalability, accuracy, energy, and performance for pattern recognition applications.