Impala cuts off at will

I am the second owner of a 2000 4dr Impala. My mileage is 107K, automatic, 4 whl drive. The car began to randonly cut off three yrs ago around 85k. Then it only would do so in cold temps with the heat high. In june 2005, it would cut off on hot days. I have been to three chevy dealerships & the car was in the shop for all of 2006. The battery light comes on and the steering wheel get stiff. Sometimes it starts right up and others it takes a while. It does not make a sound when it cuts off. When trying to start it up, sometimes I cannot hear the fuel drop in the back. The dealers have replaced the: oxygen sensor, catalytic converter, transmission sensor, fuel pump, reset the computer. The car has a slow oil leak and increasingly shuts itself off.
I went to Branch Electric to run tests and nothing came back. The check engine light usually comes on once the car cuts off. Sometimes it stays on, other times it goes out. When the dealer read the codes, it was a different set of codes each time. One time they drove my car, it cut off and he wrote down the codes. Got to the shop literally five minutes later and an entirely new set of codes appeared. (Thus resetting the computer)i love my car, it is the first I purchased on my own, please, please, please help me.