One of our foster kids had the exact same issue. We tried to be subtle but it just didn’t work. It came to a head when she asked me to help her dry her hair. She’s got out of the bath and it was wet but it was FILTHY at the roots, thick matted and greasy. She claimed to have properly washed it but it was clear she hadn’t. I checked the shampoo bottle as we’d brought her one of our own choosing when she had moved in 5 weeks before. It was still full, as was her bottle of body wash.
I sat her down a few days later and had a long chat with her about it. I was honest to the point of being brutal about how she smelt and the impact that had on us all. I reassured her of her love and that it wasn't her fault. She had been in care for 3 years (on and off) and this was the first time anyone had actually asked her if knew how to wash - she didn’t. She thought washing was getting wet. No-one had ever taught her anything different and she hadn’t picked it up for herself as at "home" there had been no routine, no soap and usually no hot water.
Sitting in our living room, I demonstrated the amount of shampoo etc she’d need, how to wash her hair, how to wash her body etc. For weeks after I’d linger outside the bathroom shouting things like “Have you put shampoo on your hair”, “have you used the body scrubber, with the soap?” etc etc. On several occasions she'd get out and I'd smell her and send her right back in. It was harsh but as she admitted it was impacting her friendship at school (she was the class smelly kid) it was worth it. We also brought her loads of good strong deodorants, Mitchum was her favourite. Enough roll-ons and sprays to keep some in the bathroom, others in her bedroom and in her various school bags - meant there was no excuse for forgetting or not being able to find one.
We also discussed washing clothing. She was used to wearing the same things for days and would keep the dirty clothing under her pillows only for it to be put back on a few days later.
It was not a quick fix but things are greatly improved and generally she is very good now. Its been 2 years and the only problem really is still forgetting to brush teeth, and if there is a change to the routine (eg school holidays). We have a “bath” timetable on the wall, to remind all the kids which days they go in, and I still have to ask if everyone has brushed teeth before we leave the house as at least one child will forget.
My advice is to be honest, understanding and patient – but most of all be persistent. The situation won’t change overnight and you’ll need to work to instil the proper routines. However its also something that is pretty easy to sort compared to some behavioral or emotional problems.
Good luck!