Check the axles and man handle them and see how much in and out slop there is. They won't be perfectly right but they shouldn't be sloppy. It depends where the noise is coming from. The noise could be your flex discs, center support, beating. Most likely the diff mounts if of its the rear end. Check all those and report back

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Only diesels in this driveway.
2005 E320 CDI 243k Black/Black
2008 Chevy 3500HD Duramax 340k
2004 Chevy 2500HD Duramax 220k