Oiling usually means you want to use the Vlies Pads from Festool, they offer them for their Oiling system, Surfix. Green and White pads, different grits between the 2 colors.
You're burnishing the wood surface with the pads and the oil, wiping the surface, letting it dry, and doing it some more after that depending on what level sheen and surface you're looking for.
You can also do something similar with Platin 2, but I prefer the Vlies pads/discs for an Oil Finish.