White smoke out of exhaust/burning oil

1995 Acura Integra GS-R DOHC VTEC 130,000 miles: I bought the car from a dealership and about a week after I got it I saw white smoke coming out of the exhaust. We thought it was the oxygen sensor so we got it replaced but it still does it. When I shift, heavy white smoke comes out of the exhaust, but only when I shift. The smoke smells like gas and burnt oil. I have been through 4 quarts of oil in a matter of a week. Its not a blown head gasket because I am not loosing coolant. Then today I found a little puddle of oil where my car was sitting over night. The mechanics here cant find anything wrong with it so now I turn to you. I use this car to deliver pizzas and I cant afford to keep putting oil in it ever two days. Please help me.


-Rick