I've never played LBG enough to even think about calling in an arty (artillery) strike, but I will answer for LB2 (should be almost exactly the same). Arty strikes are not really very effective, especially if the target starts moving. Generally I've found that the arty will come down until the designated target is destroyed, if it is stationary. It would make sense to try and target a cluster of tightly-packed targets, although most of the time the arty appears to be very loose with accuracy and spread. And to make things worse, there is absolutely no 'splash' damage done by the arty rounds - so there must be direct hits, even on things like tents.
I would never suggest to use arty on point targets other than say, a bunker - something big and tough. If the arty acts anything like it does in LB2, it's best for just keeping the enemy's 'heads down', so to speak. Unlike in real-life, an arty bombardment won't stop the enemy from firing, but it will disperse a group of threats and make their accuracy and effective rate-of-fire arguably lower. This then gives you a bit more time to clean up with Hellfire, MPSM rockets and chaingun (although I know that wouldn't help you as you called in arty when you'd run out of ammo).
If you find yourself in a mission with multiple threats - too many for the amount of ammo you have - you really need to use strategy and think before you deploy any weapons. Try and avoid as many threats as you can on the way to the mission area and keep your weapons for the mission priority targets, THEN, use up any remaining weapons on the way back.