If there is is no visible oil leak, then the oil must be getting burned in the engine.
You don't say which engine you have, so I will just give a general answer.
There are 3 possibilities that I can think of that would cause a significant oil loss-
- Worn/damaged piston rings or cylinder walls
- Turbo bearing worn
- Cylinder head gasket leaking between oil and cylinder
- Valve oil seals/guides (to a lesser extent)
I would think that a leaking gasket would be the least likely, but still a possibility.
Checking the condition of the spark plugs (if there are some) may give you an indication if there is an issue with one or more cylinders being worn. The plug may have oily black deposits on them. If so, the only fix would be an engine rebuild.
The turbo could be leaking oil into the air intake. You could remove the pipe that goes from the turbo to the intercooler to see if there is oil in there. To fix this you may be able to get the turbo rebuilt or replaced. If the engine uses diesel, it would be a good idea to check this soon, since if the leak gets too bad, the engine could start to use the oil as fuel which can cause it to run out of control - https://www.youtube.com/watch?v=i3wxQkZS0UA
You could try using the thickest grade of oil that is recommended in the car owners manual. That may slow down the rate the oil is burned.
As suggested in the comments below by David, oil can also get passed worn/damaged valve stem oil seals and guides.