You probably know that oil lamps burn better when the oil level is higher rather than lower. I don't know why, but my guess is because the oil does not have to be pulled up so far to burn.
Yet it can take a lot of kerosene to completely fill the reservoir of a lantern, and if you have a bunch of them throughout the house like I do, that's a lot of kerosene!
Years and years ago, my father in law shared a trick that I'll pass along. This only works once the wick is thoroughly saturated with oil. You don't want to try it if the wick is dry. What you do is, put some oil in the reservoir, then add water to bring the level up to where you want it. The water will stay at the bottom, while the oil will be at the top, where the wick can get at it. As the oil burns down, add more.
An unsaturated wick will grab any liquid it can find, so make sure it's saturated with oil first before it gets the chance to grab some water. You don't want it to grab any water.