Rubbing some baby powder into the greasy areas will help. Mosi had slightly greasy fur for a while when he was younger.
The fur at the base of his tail and on his back got slightly greasy from about 4 months. I guessed it might have been a slight case of stud tail but I'm not sure. I also don't know whether or not that can affect other areas, but I'd guess it could, and I think Leo is about the same age as Mosi was. It continued for a while after neutering but soon stopped and he doesn't get greasy fur at all now.