2003 Jeep Grand Cherokee Overland 4WD Engine cuts off at idle and low speed driving, particularly when turning right. Acts like it is running out of gas but tank is half full. Will restart and run short while and cut off again. Error codes P-320,P-340,P-1391.

4.0L
what transmission, mines a 5 speed stick so?????
idles good, well that dont take much.
will only move, car moves?
with what wide open ,the throttle?
well just barely throttle is normal, why say that?

my guess is car has low power, or can not go fast in all gears.
is that it?
if yes, that is transmission slip or a weak engine,
transmission slip is easy RPM goes way high car dont move
weak engine acts like brakes stuck on , low RPM deep right foot.
post all symptoms and win, big time.

find noise location first. never ignore noise on machines. and 10x that on man movers. 100x that in the air.

then scan it. using any obd2 scan tool,
a tool that does Jeep factory codes. 10x that.

take it to the nearest dealer that is very dangerous. there may be a recall on this problem

Need more information. Is the engine hot or cold when it shuts off ? Does it do it when idling or when driving ? How long do you drive before it acts up? High speed or low speed Please describe the symptoms with more information. Problem could be anything from water in the gas to bad fuel pump, bad spark plugs ,fuel filter, injectors or ignition coils.

check the tps and iac on throttle body

spray carb cleaner to cold intake a see if the idle changes this is a way yo look for a vacuum leak

Turn off the AC system and see if this stops, it may be due to the AC compressor cycling rapidly due to a low charge of refrigerant..

I would replace both your cam position and crank position sensors. one is probably bad with an intermitant short. but they are both cheap. $50 for both from rockauto.com. Forget about the fuel filter, you are good there. You should be able to find instructions on replacement at autozone.com

drivers side front of the engine i believe it is on the timing cover but the camshaft tone wheel is on the left side head.

Ckean throttle plate inside throttle body...They tend to get dirtier than their counterparts in carbureted engines due to lack of fuel spray that kept them clean. If no luck with that, clean idle air control valve on TB. When doing this, don't turn the plunger, just clean with carb spray and replace. do not loose "o" ring seal.
Good luck