A transition to self-sustained current oscillations was investigated in a circuit with a NbO x thin film device, acting as an artificial neuron. Above a threshold of the applied voltage, the circuit begins to demonstrate persistent but rather random current spiking, which becomes more regular with increasing applied voltage. Experimental measurements reveal two scaling regions of the interspike interval dependence on source voltage: an initial logarithmic dependence which transitions to a power law with exponent -1/2. Using a numerical model of the artificial neuron circuit, we observe good agreement with our experimental data. We show that the logarithmic scaling behavior is associated with noise-induced spiking, whilst the power law is attributed to noisy self-sustained oscillations which would exist in the system even with the absence of noise. These findings stress the importance of noise in the dynamics of NbO x threshold switches and shed light on their spiking response to variation of the input signals. The reported approach to spiking control in NbO x artificial oscillation neurons can help to develop an optimal design for neuromorphic neural networks and oscillator-based computing systems.