Yes, this can be harmful. Give the bird a bath in lukewarm water and use Dawn dish washing soap. Just rub a small amount of watered down Dawn soap into her feathers and rinse, rinse, rinse. The bird will be soaking wet when you're done so dry her thoroughly and keep her nice and warm until she dries completely. If you don't think you can bathe her, get her to an avian vet asap for a bath. It's important to get this oil off her asap! Best wishes.
The best answer to any question regarding a sick pet will come from your own veterinarian, however, I am happy to provide information based on my experience.
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