Since we are talking oil here, my old sensei suggested sanding off the factory varnish type coating and using walnuts wrapped in a cloth to "oil" the bokken. He said it helps prevent the splintering when the bokken is dented.
I use walnut oil from a bottle so using walnuts in a cloth seems fair enough. The reason for oiling is to keep the outer layer of the wood springy and not allow it to become brittle. Here in the UK where the weather can be humid one day and dry as a bone the next a bit of oil about once a year is the norm, same as the maintenance required for a cricket bat. In more even climes you might get away with one treatment lasting for several years. I usually put a fairly even coat of oil on my wooden weapons and leave them for a couple of hours, then it is cleaning the excess off with a rag, then paper to really get any surface oil off. When it is done there should be no trace of oiliness at all, just a smooth, resilient finish.