Your sentence is very clear and easy to understand, but it can be made a little better by fixing grammar and adding a little more detail.
Corrected sentence: In winter, people hang bird feeders to give birds food and help them stay strong.
Explanation:
- Instead of saying and keep them strong, it's better to say help them stay strong because keep needs an object that shows what is being kept.
- Help them stay strong clearly shows the purpose of giving food to birds.
- Everything else in your sentence is good!