I have a 2003 saturn Vue AWD V6 i'm getting error codes PO700,PO335,PO421,P2119,PO102,PO37,PO57,PO44,PO431 when it gets to operating temps it will shut off if left to sit for 30-40 mins it will start again. will even shut down when driving. if i can get past this point that takes a min or two after running for 10 mins will be fine till it sits again for a couple of hours.

PO700 is a code telling you there are codes in the TCM of some late model cars where the Transmission control module has been removed from the PCM the vehicles main computer , And basically it happens when the TCM has a issue within itself or the transmission that sets a code and it sends a request for the PCM to illuminate the SES or CHECK engine light. To get at the TCM codes requires in most cases the most up to date scanner software purchased after the cars model year and as of yet is still a little iffy. Standard OBD11 scanners will generally not be able to see these codes.

P0335 (Crankshaft Position Sensor A Circuit Malfunction) first disconnect the CKP itself and inspect the connector and terminals for corrosion. It should be clean and dry. Make sure the weather-tite seal on the connector is in place, uncontaminated and undamaged.
Resistance of the CKP should be 500-900 ohms.
If all good, trace the CKP harness upwards as far as you can (until it enters the main harness) and make sure you don't have any "rub-through" or spots where the wiring appears damaged.

DTC P0421 Warm Up Catalyst Efficiency Below Threshold (Bank 1)
DTC P0431 Warm Up Catalyst Efficiency Below Threshold (Bank 2)
Its too coincidental for both catcons to fault so there's something in common to this error (I feel is) upstream. First there's a V6 engine with separate sets of cylinder banks serving separate catcons with separate pairs of O2 sensors. For both rear sensors to come up simultaneously indicating low efficiency and "runs fine but strong exhaust smell, maybe running rich(?)" suggests a component in common to both cylinder banks; maf, map, iat, ects, tpp, etc.. Any one of these parts plays a role in the overall effect of a running engine and most likely needs monitoring while the engine's running with either Saturn's Tech-tool II or better readers/scanners capable of displaying live data to discern subtle faults translating to either a constantly rich or leaned out condition, abnormal running. Without other error codes to go by, there may be no choice than to seek Saturn diagnostic services other than a local expert capable of interpreting all the information from live data displayed onto a graphics screen to read from all the sensors. Diagnostic specialists.

P2119- THROTTLE CLOSED POSITION PERFORMANCE
Possible causes of DTC P2119: Weak throttle body return springs
Throttle plate sticking due to carbon build-up.

P0102 code relates to the Mass Air Flow (MAF) Sensor. The mass airflow sensor measures the speed and density of the air entering the intake manifold. The engine computer converts this input to a Mass of air per unit time to correctly fuel the engine. the code P0102 will set if the MAF sensor signal voltage is less then 0.20volts.

Code P0507 will set if the actual idle speed is greater then 200RPM from what the engine computer has commanded. Possible causes for this code: P0507 is high idle when the PCM wants lower. If you have the 1.9 LT SOHC engine in the 2000-2002 year range this is normal caused by a leaking intake gasket. Can be other sources of vacuum leak or something else that keeps the RPM up when it should not. It may be the Idle Air Control valve sticking.

The other two codes P037 and P044 i an not sure and the code P057 was a guess of P0507 since it's seams to be in the area where the problem is . The P0404 i am guessing it's going to be EVAP problem like a lose or bad gas cap. P0370 is (ECM) replicates the signal received from the crankshaft position (CKP) sensor. This signal is sent to the fuel injection control module (FICM) through the engine speed signal circuit. The FICM uses this replicated signal to generate injection current and control the recharge of the fuel injection high voltage circuits. When cranking, the FICM has full control of the fuel injectors. The only input the FICM uses at this time is the engine speed signal from the ECM. The FICM monitors the signal along with the injection request signals from the ECM after the engine is running. If there is a problem with this signal, a DTC could set.

Start with the simple and clean the Idle Air Control (IAC) valve, and the Mass Air Flow (MAF) sensor. This may help the P0421, P0431. and then check the crank shaft sensor wire harness and replace the sensor, which should take care of the P0370. *** for the P0404, check the gas cap if not replace it. Good luck and keep me posted.