Burning oil or losing oil ?? If your losing oil check your gaskets and any
part of the oil circuit. If it is burning oil how old is your car, buring
oil is a sign of worn oil rings, and the oil is passing over the ring and
being burnt. This is only fixed by replacing the rings. If it is a oilleak
coming in contact with heat, once again, check your oil circuit. for any
leaks and seal.

Peter

Well you didn't state the miles on the car, but he's my advice.

If your always seeing blue smoke out your tail pipe, it's most likely
the rings.
If you only see the blue smoke after accelerating hard, then taking your
foot of the gas pedal, then it's most likely your valves.  A head grind
is generally not that difficult.
If you have a cylinder compression guage and know how to use it, you
could try the old oil in the cylinder trick.

1. Remove all spark plugs
2. Measure the compression in each cylinder, and record
3. Add about a tablespoon of engine oil to each cylinder, one at a time,
via the spark plug hole, and measure the compression again, in that
cylinder.

If the compression goes up, your rings are leaking
If the compression doesn't change, your valves are leaking.

There is no magic potion for a worn out engine, or broken rings, or worn
valve guides.  They need to be replaced, or repaired.

If that eclipse is a 2.4, and is not terribly high mileage I would be
very suspicious of the valve seals. Those were a weak point on some
2.4's of that vintage...