Sounds like a bad subframe mount when u start or stop cuz ur frame slides ever so slightly when you take off on a bad mount...or could be a strut mount, Im sorry but ive never heard of a neon w/ 46000 mi on it with bad cv axles or half shafts. Only w/ a 100000 miles have I experienced it. The strut mounts could easily go on it first if u live on or around bad roads like if you live in oregon which is absolutely the worst highway ive ever been on in portland, then it will happen a lot sooner then say on a fresh smooth road. Same is true w/ the subframe mounts. You can drive on bad cv axles and never notice clicking noises until you have axle grease sprayed all over your tire well.

 

Oh under a high load you hear clicking? How bout from a cold start? Could be your crankshaft bearings, you might have one on a roll id get under there and check it out immediately find the spacing w/ a mircometer. Or just could be a lifter sticking but itd be more like a tick tick tick instead of a click... or like a rock in your tire...I wish you could record the sound and upload it in here but we cant hear it so we cant exactly diagnose it too well...