If I were you, I would start by washing the ceiling to see what you really have and I would wash with a mild soap like Ivory or Murphy’s Oil Soap. Unless there has been a lot of dust, dirt or smoke in the room, that’s the safest way to see what you really have. Cleaning would be the first step in any repair process anyway.
I think that I would then wipe down the whole ceiling with lemon oil. Lemon oil is mostly mineral spirits with a little lemon scented chemical that didn’t actually come out of a lemon but covers up the smell of the mineral spirits. The mineral spirits is a solvent that may reamalgamate the surface a bit. The mineral spirits is also flammable so do this with good ventilation and with no fires, sparks or electrical apliances including lights or fans operating. And leave the rags outside and unfolded for a couple of days and until they no longer smell like the mineral spirits. Follow all the label directions.
Other than a very few woods, like teak, wood does not have or need oil. The woods that have oil have so much that they never really need a refill, they just need a cleaning so the oil can get to the surface. And just like the oil in your car, oil attracts and holds dust and dirt, something you want to avoid on your wood surfaces. Tung oil would not be my choice.
Henry in MI