The Tower 55 models were made by Ajin Precision of Korea and were imported by Overland Models. Jerky and noisy operation is definitely NOT normal for one of them. I have two and they are extremely quiet, smooth runners.
It sounds like you need to lubricate the model and the decoder may need to be reset to factory defaults and be reprogrammed. The decoder is a Digitrax Sound FX. I ripped that decoder out and put Quantum Revolution sound in both of mine because I did not like the sound, but the motor control was very smooth with the Digtrax decoder (and is even better with the Quantum).
Other things to check:
Clean the wheels and track.Check electrical pickup connections at the trucks and decoder. If the decoder uses the plastic clips to hold the wires in place, remove them and solder the connections.Make sure your controller is set to 28/128 speed steps.Turn off DC operation in the decoder by reprogramming CV 29.
No they should not turn in that manner.
I have a friend's T55 ES44DC on my workbench right now with the identical problem. The problem is that the worm gear is split on the shaft. Thus the shaft turns with the motor, but with weight on the truck, the gear will just sit still while the shaft spins inside it. I'm trying to figure out if there are parts available for the T55 drives, or if there is an appropriate NWSL gear to use.
None of that sounds normal and the locomotive does not sound like it was "new in box". I have several of them and none have had any of the problems you describe.
I've heard that some Tower 55 diesels had a problem with the gears stripping. Since you say the wheels can be turned by hand, I'm guessing that's what the problem is. You should never be able to turn the wheels when they use a worm drive.
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If you have an Athearn model you can temporarily remove a gear from to see if they are the same size as the Tower 55 gears, you can get replacement gears from Athearn.