Nanodevice oscillators (nano-oscillators) have received considerable attention to implement in neuromorphic computing as hardware because they can significantly improve the device integration density and energy efficiency compared to complementary metal oxide semiconductor circuit-based oscillators. This work demonstrates vertically stackable nano-oscillators using an ovonic threshold switch (OTS) for high-density neuromorphic hardware. A vertically stackable Ge0.6Se0.4 OTS-oscillator (VOTS-OSC) is fabricated with a vertical crossbar array structure by growing Ge0.6Se0.4 film conformally on a contact hole structure using atomic layer deposition. The VOTS-OSC can be vertically integrated onto peripheral circuits without causing thermal damage because the fabrication temperature is <400 °C. The fabricated device exhibits oscillation characteristics, which can serve as leaky integrate-and-fire neurons in spiking neural networks (SNNs) and coupled oscillators in oscillatory neural networks (ONNs). For practical applications, pattern recognition and vertex coloring are demonstrated with SNNs and ONNs, respectively, using semiempirical simulations. This structure increases the oscillator integration density significantly, enabling complex tasks with a large number of oscillators. Moreover, it can enhance the computational speed of neural networks due to its rapid switching speed.