The state of oxygen in aqueous supersaturated solutions prepared by different methods was studied using high-resolution ultrasonic spectroscopy in combination with other techniques. This allowed for nondestructive evaluation of the properties of oxygen solute particles, composed of oxygen molecules and surrounding (coordinating) molecules of water, at equilibrium, supersaturated conditions, and different temperatures and concentrations of O2. The results were compared with the behaviors of other types of solutes in water, including H2O2, which has similar molecular size and mass to O2 but is characterized by a significantly different type of interaction with water molecules. Additionally, theoretical modeling was performed to assess the ultrasonic characteristics of dispersions of oxygen nanobubbles stabilized by a surface electrical charge. The obtained data indicate a clathrate-like organization of water in the coordination shells of single molecules of O2. We did not find any signs of formation of clusters of oxygen molecules in supersaturated solutions. No quantifiable presence of oxygen nanobubbles in the solutions was detected. The state of O2 molecules was not affected by supersaturation within the analyzed concentration range of oxygen. The results also demonstrated the potential of the ultrasonic technique in precision real-time nondestructive monitoring of oxygen solubilization and outgassing processes.