Hello, if the car is using oil and there are no leaks, then it has to be burning it in the combustion chambers. This is normally a sign of broken or worn parts like piston rings. The best way to get an idea of the problem in your case would be to do a wet and dry compression test and then maybe follow that up with a cylinder leak down test. If you check the cylinder compression in the cylinders and write it down and then go back and squirt some light weight oil into the cylinders and check it again, if you see a sizable increase in the readings, that is a pretty good sign that the piston rings are worn. As, when you ad the oil to the cylinders if the rings are worn, the oil will tend to make a seal between the rings and the cylinder wall and that will raise the compression because there will be much less leakage of the compression past the rings. Doing a leak down test will help to confirm the problem. You remove the spark plugs
and with the aid of a measuring device available at most parts stores, you bring the cylinders up to top dead center one at a time and then inject compressed air into the cylinders and measure the amount of leakage of the air pressure being induced into the cylinders. Then you listen to see where the air is escaping from. If you hear air in the crankcase or out of the oil cap hole, the problem is with the rings or pistons, if air escapes out the exhaust
you know there is a problem with the exhaust valves, if it comes out through the intake or carb or throttle body, you know the intake valves are leaking and if you get bubbles in the radiator
or air out of the cooling system that points to a problem with the head gasket
sealing or a crack in a cylinder or cylinder head. Hope this info gives you a little more in site into testing to find out where your oil is going thanks.