My hair was oily as a teen (not anymore). Use a shampoo for oily hair, don't use any conditioner, and only shower in the morning (also no gels, etc.) She might be sweating in her sleep at night, which would make her hair more oily. Perhaps you could try scrubbing the shampoo into her hair and washing it in the sink as a test to see if maybe she isn't scrubbing it at the scalp well.