There is no reason to believe that the products actually deliver oxygen to the body. It is possible to use an electric current to add a tiny amount of oxygen to water, but to access it, a human would need gills. Even if they could, taking oxygen into the stomach through a liquid, pill, or food would not significantly raise the body's blood level of oxygen.
Oxygen enters the bloodstream through the lungs.
The body adapts to what it needs by changing its breathing rate. If enough oxygen is available to sustain life, the body will extract what it needs from the air and deliver what is needed to the cells. Blood returning to the lungs contains surplus oxygen. At least a dozen companies have marketed such products. The FTC says that the product appears to be nothing more than salt water.