Blue Smoke from Tail pipe while accelerating

Dear All,

For a few days I have been observing blue smoke from the tail pipe while accelerating. Only once I removed my foot from the acceleration pedal it did not give any smoke.
Also when I keep on pressing the acceleration pedal for long, it only gives the smoke for two to three second at the beginning and then disappear still with high acceleration.

My car is using engine oil (Half of total with in 1200 kms), but when the engine oil goes on the middle of high and low level of dipstick it does not use engine oil anymore and has no smoke with high acceleration.

I consulted with many local mechanics and all suggested to get complete overhauling of the engine which is not worth it for me as the car is already too old.

Can anybody suggest me the solution for the same or do I need to get a complete overhaul?

Thanks in advance.