You have left out a lot regarding her home life, which you may not know about.
For instance, does she have two parents? How many siblings? If they are a poor family on food stamps remember that soap, etc. are not available with food stamps. Food pantries seldom if ever have soap, toothpaste etc. Few people realize you can brush your teeth with baking soda.
Is there a washing machine available in her home or do they have to pay to use a laundrymat? Few people realize you can "wash" your clothing without soap and adding a little vinegar or lemon juice to the rinse cycle can help remove the musty, sweat, scent from clothing.
I am surprised the school she is attending has not addressed hygeine with her. Even our grade schools here in Danville will address this issue with the children.
If many of her clothes come from "thrift shops" it may be difficult for her to dress in clothing that is up to date and stylish. It may be her clothing comes from donations and people seldom donate such items.
Have a makeup party for the girls in your church group and make part of the party a lesson on good hygiene. Demonstrate how you can clean your nails, etc. without the use of nail files etc., make it a type of game so all of the girls will enjoy it without making her feel singled out. One of the games could be a select an item from a tray that can be used in place of toothpaste, soap, etc.
If you know any Avon, Mary Kay, etc. representatives talk to them about donating products that have been discontinued for your party/this family. Believe me, they have products like shampoo, shower gels, etc. that have been discontinued in stock and will get a tax credit for donating them. It will give them a good home for the no longer saleable items and lessen the clutter in their stock areas. In this way she will be able to get makeup, face creams, shower gels and colognes, shampoos, deordorant etc. and you can give them to her at a special time when gift giving will not look insulting to her, like making them prizes for the most improved look, etc. at your party.
You can always invite her to your home with the request she could help you do some work and talk to her privately about the issue having her help plant a garden, clean out the attic or basement, etc. Her payment could be personnel products and or clothing. Good Will has some nice things very reasonably price. Dollar Tree, $.99, etc. have makeup, soap, shampoo, manicure items, etc. and all are $1.00 each. You could even take her to the store after the work is completed and let her pick out the items she really likes in leiu of paying her cash.
Take up a donation at your church circle for hygiene items, soap, tooth paste, shampoo, detergents etc. and donate them to her and her family.
The public library has a section of books on hygeine you may want to look into.
P. R