This is more a mechanical issue than electrical or fuel. Do the leak down and compression test, a rebuild or a good used engine may be in your near future.
If this is a 2.4L they are known for oil use. You probably have stuck rings on that cylinder. I would do a leak down test to rule out valve sealing but not likely.
Yes, that should be the 2.7L, although at this point it's not sounding any different. OP, you say it's been burning oil since last summer; is that by any chance the time you got this car? Or did you buy it new?