How Do Air Stones Increase the Oxygen in the Aquarium Water?
As for increasing the oxygenation of the water, the best thing air stones do is provide good water circulation. So if your filter is adequate to the tank, it will already be providing adequate water circulation. The benefit from an air stone and air pump will be minimal and unnecessary.
The air stone will increase the water circulation more than an undiffused air feed into the tank from an air pump, and the bubbles themselves will also increase the surface area of the water more, but the real benefit from an air stone as far as oxygenation goes is just the increase in circulation.