oil always gets low and I have to add 1 qt per 1000 mile, whats the problem??
Couldn't find any oil leakage, the exhaust air is fine, the same brand MOPAR oil has been added..
The car has recovered recently from a bad head gasket and everything went fine except the oil..
total run of 73000 mile
engine of 3.7l

Hmmm. Well, the laws of thermodynamics says it has to go somewhere. Some options might be:
1) Physical leak. I'd look first at the oil filter gasket where it meets the engine, the oil pan drain plug (loose?), and the oil pan itself. It could be the RTV seal is leaking between the pan and the engine, or that a small hole has rusted through your oil pan. If the leak is small, it might only drip when pressurized (driving) so you might not see a puddle of oil on your driveway.
2) Burning oil. A bad head gasket or worn piston rings might cause this. But gray-blue smoke when accelerating would be the main symptom, and you said your exhaust doesn't smell like oil.
3) Oil in the coolant. Another option with a bad head gasket is that the oil pressure could force some oil into the coolant passages. If so, your coolant level in the bottle will rise, and it will become sludgy, like a coolant/oil milk shake.

Sounds like you're looking at the right things. It makes me wonder if the head gasket repair was done properly. Let us know what you find. I'm also curious if there are other options I haven't thought of.

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Jeepin By Al 4" Lift Kit
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Thanks for ur reply,
well the coolant level is the same and no sign of oil down there..
I might think about PCV system cause the oil look like having a black line, so it may not actually burning inside the piston which is caused by worn rings. In fact I'm thinking about oil is escaping through the valve without burning thats why smoke is not clearly found..
Does my theory sound applicable??

Possibly a stuck lifter. Mine is doing the exact same thing. Oil in the emissions but nothing in the drive. Maybe a slite tap at low rpms?

Sent by using tin cans and string

With my 07 I have same issue. I noticed blue smoke at startup after my car has been running awhile then sits for a short time (no smoke at morning start up). Looking into Valve seals