Thank you for thinking of this girl's needs when she could so easily get lost in the shuffle of the holidays!
I like the ideas other people had about inviting her to dinner over the holidays so she has "family" around her and doing the grocery store/Walmart gift cards to help with groceries and the such or even a gas card with enough $$ on it to last for a few months.
Here's an idea that I didn't see mentioned. I've read about this being done but with privacy issues, I don't know how easy it would be to do, but if you aren't hurting for money yourself and can afford it, maybe annonomously pay rent for a few months for her (or a year of utilities???). Her landlord (if you explain your idea in detail) can probably find out for you where she gets electricity, water, trash, TV, etc. If I was down on my luck, that would be where my need would lie the most...maybe if she didn't have some of these bills, she could go down to just 1 job so she can be home more with her sister. Also, health insurance costs?
So this is not just a one time gift for the girl, you also might consider, each time you go grocery shopping, consider buying double of things...especially the more "luxery items"- toilet paper, paper towels, paper plates, nicer foods, fruits and veggies...more expensive items she may be trying to skimp on to save money or some of the staples all families need and then drop it off to her on the way home and you can "see how she's doing".
Sorry...lots of ideas, but what about a "coupon book" you make for her with little needs like..."good for week of deep cleaning your apartment" or "good for childcare for your sister so you can have a night off" or "good for your favorite meal made hot and delivered directly to your door".
As you get to know her more, you may be able to discuss with her about some of her needs and some of the local programs, such as Medicaid insurance, WIC for help with groceries, things like that and offer to drive her and go with her to these places. You can step in and be "mom" when she needs it- I had several of these type of women in my life and still remain good friends with them and remember all they did for me, the meals they invited me over for, the conversations we had! Don't let your son make you feel "nuts" about this...it is a wonderful thing to do and your son should consider doing a "secret santa" for her with some of his buddies or clubs at the school!