Sometimes the best gift you can give someone is to listen. It is easy for those struggling at Christmas to feel forgotten as everyone is busy planning for their own families and friends. It might be as simple as popping around to share a coffee. You may notice something you could do to help ease the load while you are there - like do their dishes, offer to baby sit or give them a lift to the shops.
Just the acknowledgement that you care and are willing to spend time with them could be enough to lift their spirits and motivate them to find answers to their problems.
If people are fortunate to be comfortable - perhaps instead of giving each other presents you could pool your present money and buy Christmas dinner and presents for a local family who are struggling financially.
Finally, one of the best things I have ever done to help myself is to volunteer - including when I have been alone in a strange country for Christmas.
There is something so uplifting about working hard to help others in need. I spent one Christmas serving meals for the homeless and lonely and it was a wonderful experience for everyone - I didn't have time to feel alone!