03 Rally Lancer stalls out randomly and has no acceleration during cold weather

My girl has an 03 Rally Lancer, its had its usual maintainence and her ex took out the o2 sensor a few years ago. Well since I have known her, her car stalls out randomly for no reason at all while sitting at a red light and during cold weather i can accelerate to driving speed no problem, but when you try to punch it to pass a car or whatever its like there is no power at all in the engine and it makes a no wierd sounds but you dont really hear the engine rev up at all. You have to accelerate nice and slow. Well thank you for any help.