Hi Op, when she does use conditioner, tell her not to do all her hair just the ends, not the roots. You will notice that hair stays cleaner much longer and doesn't get as oily.
A gentle exfoliater would be a good start since she is only 10. I have very oily skin when i was young and the "gentle" exfoliater's never did anything so i switched to St Ives which was much more coarse and i still use it twice a week. But ur 10yr old is too young for that.
Also Clinique has wonder moisturiser's that are not oily! I know its expensive but it could last up to a year. Mine does because i only use a pea size amount. The moisturizer has like a gel feeling and dries almost instantly.
Hope this helps.