If by "oil" you mean lamp oil, then kerosene and lamp oil are the same thing. Lamp oil often has aromatics added, but in the end, they are pretty much the same base product. The price of kerosene varies depending on where you buy it and how much buy. Buy at a bulk oil seller and you can get it really cheap. Buy it in a fancy pants lamp store and you will get ripped off for sure. It is also very similar to JP4 (jet fuel) so if you have access to an airport FBO then you can get it quite cheap there.
Coleman gas lanterns or lamps generally burn white gas, which is pure gasoline without any additives at all. Some burn propane, some kerosene, and some duel fuel units burn white gas or unleaded gas. Never, but never, burn unleaded gas inside. If well tuned, pressurized white gas, kerosene or propane lanterns burn very clean with almost no CO. The purists amongst us, prefer the white gas or kerosene lanterns; propane is for neophytes who don't know how to light a liquid fuel lantern.
As far as burning fossil fuels in houses goes, remember that our grandparents, great-gandparents, or in my case me, as a child, grew up in houses that were lit by fuel burning lamps, both pressurized and non-pressurized. These days we seem to have a phobia about burning lamps in houses, but then we now have phobias about guns, knives and wild animals too. Coleman recommends a 6 sq. inch exterior window or door opening for each lamp burning in a room. They also recommend that you do not bring lamps indoors until all pre-heat combustion has completed and the lamps are burning hot.
The same applies for Coleman stoves, but give a larger fresh air opening and be aware that any gas stove, including the natural gas stoves many of our houses have, give off more CO when burning against a cold object like a cold pot of water. As the water heats, the CO given off decreases because combustion is more complete.