I have a couple of clocks and have yet to get one cleaned and oiled which needs it. From what I understand, they use whale oil on clocks due it is qualities for this application. It is rather expensive and if you go to a reputable clock shop, they should also clean it aiding in it running well. If you have another clock shop in the area, get a second opinion and ask what will be done for "an oiling".
I seem to recall this general subject being discussed on this website some time ago, but I am not sure what the string title was or which forum it was on, or if it still exists after some changes took place.