This is the first time I heard of cylinder deactivation because of burned oil. I don't know if that really exists. I do know that they can deactivate cylinders when they detect a misfire. They cut fuel injection to reduce unburned fuel reaching the cat. You could do a compression and leak down test to possibly disagnose physical engine damage that could cause oil burning.
The first step should be in my opinion to get a new (or used one confirmed working) MAF sensor. Without it the car won't run right and any disgnosis might be falsified.
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