The OP reports the car starting but spluttering to a halt from cold and has three codes relating to O2 sensor reading being too lean / out of spec. Going with the symptoms and info the car is giving this logically suggests either O2 sensors are down causing bad fuelling OR or there is a vacuum air leak on the intake side causing over-lean fuelling or metering. Its an M54 engine which is famous for split hoses and boots around the intake system and MAFF so that's where I would start first, hopefully it will be a cheap fix 