Q. We have a 1920 house with a concrete block foundation and uneven concrete basement floor. Can it be finished or should it be done by a professional?
Of course you can do it, but there are some things better left to a pro.
It would be best for a professional concrete layer to add 2 inches of concrete to the floor to make it even and level, and if there is enough head room to allow it.
You could build an insulated stud wall to the walls, but a new method would not cost that much. It is Owen-Cornings special wall that has a Styrofoam insulation covered by a special plasterboard, all just 1 1/2 inches thick, and gives all the insulation you need.
There is plenty you can do yourself: ceramic tiles (best) on the floor, painting, a dropped ceiling that attaches directly on the joists, maybe a rug on the tiled floor, and an electric heater to keep it snug and warm.
If you insulate the ceiling, it will be even easier to heat. If the cellar is dry, go for it!
Q. Is oil heat still a cheap way to heat? I have an option to go to natural gas or propane.
There is gas in the United States and Canada to last for decades, so its likely to stay cheap.
Heating oil, already costlier than gasoline, will do nothing but go up, sad to say.
Gas can be delivered pretty well as it comes out of the ground, while oil must go through a costly refining system before it can be delivered.
Gas is also cleaner than any fuel, I think.
Avoid propane, which might be as costly as oil.