Monitoring nuclear reactors is an important safety and security task with growing requirements. We explore the possibility of using seismic and acoustic data for inferring the power level of an operating reactor. Continuous data recorded at a single seismo-acoustic station that is located about 50 m away from a research reactor was visualized and analyzed. The data show a clear correlation between seismo-acoustic features and reactor main operational states. We designed a workflow that includes two machine learning models to classify the reactor operational states (off, transition, and on) and estimate reactor power levels (10%, 30%, 50%, 70% and 90%). We applied and compared five machine learning algorithms for the reactor off-transition-on and four approaches for the power level classification. We also compared the performance of machine learning models trained with seismic-only, acoustic-only, and both types of data. Five-fold cross-validations were implemented to assure a thorough evaluation of the model performances. The results show the extreme boosting gradient algorithm worked best for the first model, while random forests performed best for the second model. Combining seismic and acoustic data leads to better performance than using a single type of data. Seismic data contributed more than acoustic data for both models. We reached an accuracy of 0.98 for reactor off and on. The accuracies for the transition state and power levels are less optimal. However, our results suggest seismic and acoustic data contain useful information about the transition state as well as power levels. Seismic and acoustic data could be integrated with other observations to improve monitoring performance.