Store-bought essential oils can cause fatalities in birds. I consider store-bought essential oils to be perfumes rather than medicine. Use of store-bought EOs can kill birds almost instantly: there will be no time to save a bird once exposed.
Medical grade EOs can be entirely safe and highly effective as avian medicine.
The only two medical grade EO brands that I use and have tested in birds are Young Living and Original Swiss Aromatics. I cannot comment on the safety of any other medical grade brands.
If using Young Living or Original Swiss Aromatics, many of these oils will be completely safe for birds, in my experience. However I would never use CEDAR, THUJA or SAGE with birds due to certain specific, potentially toxic properties of those plants.
Disclaimer: These statements have not been evaluated by the Food and Drug Administration, or by any veterinarian. All information, including any product or technique mentioned, is for educational purposes only. None of the information is intended to diagnose or treat any disease.