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He may also appreciate a sand bath to roll in to help condition his coat. What type of hamster is he?
If you can get something like a chinese takeaway dish and fill it with chinchilla sand (not the dust it must be the sand) he will enjoy rolling to clean his fur up. These are essential for dwarfs really as they have such dense fur.
Another reason for greasy coat is a too small wheel where the spindle rubs the back. Often these have been oiled as they squeak and this rubs on the back as the hammie runs.
Glad he seems to be settling and hope he is soon nice and calm