Finishing oak bannister etc

For my oak (butcher block) desk, I used this polyvine wax finish in satin, they also do a dead flat version, from a few years of hands touching it for mouse/keyboard use it hasn't darkened or gone shiny ...

If you're certain that the oak is unfinished then use an oil finish, it will enhance the grain and protect the wood. You'll probably need to lightly sand the greased areas, and may need a solvent.

I generally use Osmo poly-x but recently used Fiddes for an Oak parquet floor and it looks the dog's danglies. I'll link a couple of good articles (they discuss oiling floors but the info is still useful for other applications):

I used Danish Oil very thinly applied, as many times as is needed - the more times the more glossy. And the darker the colour

soap and water and a ciureing pad wiped down and left to dry