My truck is neither manual or 4x4, however I have quite a bit of experience with 4x4 systems on chevys, and manual trans on Semis.
Seeing as the noise quieted down after filling the transfer case, and you determined it to be low, it is likely that is where a majority of the noise is coming from. If it was run too low on oil, the clutch assembly may be the source of the noise, primarily the bearings on the dog (assuming that dodges use a dog and not a friction type clutch in theirs) The chain may also be a source of some whine due to lack of lubrication if the front driveshaft isn't disconnecting.
Just fill the transfer case to the proper level with ATF+4 transmission fluid. Do not put any additives in except those specifically listed by Dodge.
A bit of whining can be expected from the manual trans, most of this is just gear noise. For most of the transmissions life power and rotation are being applied primarily in one direction, the direction that moves the vehicle forward (the output shaft and countershaft are the only ones that reverse direction under normal forwards and reverse driving, the input shaft always spins the same direction) Less than 5% of most transmissions lives are spent in reverse, and then only the reverse gear on the input and countershafts as well as the idler gear see any load, the rest are relatively unloaded. When two metal surfaces meet and rub against each other, they wear in a specific pattern. This pattern wears in such a way as to provide the most contact between the two gears, this results in quieter and more reliable operation. Because all of these gears only ever see load in one direction (given that no engine braking has ever been done on the transmission, the clutch is either engaged or its put in neutral) only one side of the gears ever wears together. When you coast in gear with the clutch depressed, the gears for the range selected are now being driven by the drive shaft instead of the engine, this forces the 'non-mated' sides together and can cause quite a bit of noise. Even if you put it in neutral, the selector only disengages the input shaft from the gears on the input shaft. All the gears are still being driven by the drive shaft, there is just slightly less 'load' on them from the input shaft bearings. Coasting in gear with the clutch engaged, also know as engine braking, will result in quite a bit of noise even in a high gear where the engine may only be at idle speed as the drive shaft is now backdriving the engine, and all the friction from the engine systems is putting load on the gear range selected.
I wouldn't worry about the trans, just make sure its filled up. As for the transfer case, if you want, you can do a fluid change to remove any debris from it (I have no clue if it has a filter, I would expect that it does, but I don't know) that may help. However, whatever damage has been done, is irreversible. As best, it just has a reduced service life, at worse, the bearings are damaged and may cause premature failure under high load. You will know if the bearings are bad or going bad though, the noise will get continually worse. But a little bit of whine is expected, just not so much that it sounds like a Honda backing up.