High-spectral-purity frequency-agile room-temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip-scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single-frequency and multi-frequency oscillators in the terahertz regime. Through optical-to-terahertz down-conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8-octaves is achieved from 330 GHz to 2.3 THz, with ≈20 GHz cavity-mode-limited frequency tuning step and ≈10 MHz intracavity-mode continuous frequency tuning range at each step. By controlling the microresonator intracavity power and pump-resonance detuning, tunable multi-frequency terahertz oscillators are also realized. Furthermore, by stabilizing the microresonator pump power and wavelength, sub-100 Hz linewidth of the terahertz radiation with 10^-15 residual frequency instability is demonstrated. The room-temperature generation of both single-frequency, frequency-agile terahertz radiation and multi-frequency terahertz oscillators in the chip-scale platform offers unique capabilities in metrology, sensing, imaging and communications.