There is oxygen dissolved in the water, and no oxygen in the nitrogen. Oxygen diffuses down the oxygen concentration gradient into the nitrogen, and leaves with the nitrogen.
If you start with a batch of water, and sparge with a large amount of completely oxygen-free nitrogen, eventually the water will be scrupulously free of dissolved oxygen. You'll also lose some water to evaporation into the nitrogen.
In a continuous contactor, the ratio of gas to liquid flow, the number and arrangement of contact stages, the effective area of the gas/liquid interface, and fluid properties affecting the mass transfer coefficient, are all important to determine how much stripping of the target molecule occurs.
It's important to realize that concentration gradients are the driver for mass flow by diffusion even if there is a pressure gradient which you might think would drive the flow in the other direction. While it is possible to make diffusion "stand still" or even to reverse it by means of a large advective (pressure difference-driven) flow of something else, diffusion under static conditions doesn't care about pressure-only about concentration. Helium-neon laser tubes contain mixtures of helium and neon in a sealed glass assembly, but over a period of years, helium diffuses straight through the glass boretube and through the glass/mirror seals and glass-electrode seals to leave the tube, because the concentration of helium in the tube is much higher than the concentration of helium in the atmosphere. The diffusivity of helium is high, and as good a job as you do to make that glass assembly impermeable, it isn't absolutely impermeable to something as small as helium. Another example is oxygen diffusing through teflon tubing into pressurized hydrogen- it can be very surprising just how much, and how fast, even those big oxygen molecules diffuse through the teflon.