A 131Xe nuclear magnetic resonance (NMR) oscillator can be used in the measurement of rotation rates, CPT and Lorentz violation tests, etc. To improve the measurement precision of devices based on a 131Xe NMR oscillator, its characteristics need to be fully understood. Under the conditions where the Zeeman interaction is much larger than the quadrupolar interaction, the characteristics of the 131Xe NMR oscillator involving the magnetic resonance, free induction decay, and closed-loop oscillation are investigated both experimentally and theoretically. The main findings are as follows. The 131Xe NMR oscillator consists of six oscillators, three of which can be directly observed by a magnetometer. When the polarization of the 131Xe spin ensemble can be described by a spin temperature, the ensemble exhibits both spin orientation and spin alignment. The spin alignment breaks the symmetry of the three main oscillators. The free induction decay signal of 131Xe depends on parameters such as the spin alignment and the driving magnetic field, which make the measurement of the relaxation time difficult. In the closed-loop mode under self-excitation, the 131Xe NMR oscillator may oscillate with more than one frequency at certain feedback gain and phase. If the quadrupole splitting is much smaller than the spin relaxation rate, then the 131Xe oscillator can be described by the Bloch equations, and the 131Xe oscillator will have a large amplitude. The oscillation frequency of the closed-loop oscillator depends on the quadrupole splitting, polarization, and various relaxation times, which should be considered in designing a high-precision NMR sensor. The results are significant for optimizing and improving the performance of the 131Xe NMR oscillator as a sensor for precision measurement.