Also, I looked into your list of oils, but I wasn't able to find any sources that I would consider credible regarding which oils are safe/dangerous for parrots. Many lists of "safe" essential oils include oils that are listed as "dangerous" on other lists.
Most lists for birds seem to agree that you should avoid tea tree oil, peppermint, citronella, and "hot oils", like cinnamon, clove, and oregano or "tree oils" like eucalyptus, arborvitae, and pine. Most floral scents (rose, jasmine, lavender) and citrus oils (lemon, orange, lime, bergamont, grapefruit) were listed as safe for birds.
Expanding the search to include information regarding essential oils used around children and cats, I found a list of oils that should be used with caution in diffusers because they are associated with mucus membrane irritation. The list included bay leaf, cinnamon, clove, lemongrass, peppermint and thyme .
And these oils were listed as best to avoid during pregnancy or while breastfeeding: Hysssop, Camphor, Parsley seed, Pennyroyal, Tarragon, Wintergreen, Wormwood
Using essential oils around kids and babies is highly controversial. General wisdom, even among oil enthusiasts is to not use essential oils on children younger than 2 years old and to only use diluted oils on older children because the full strength oils may be too potent. Other sites recommend avoiding all essential oils in children under seven years old. Feeding oils to kids is not recommended and the concentrated oils should be stored somewhere safe and out of reach. Ingestion of wintergreen oil is potentially deadly to people of all ages.
Certain oils should never be used around infants, including eucalyptus, fennel, peppermint, rosemary, verbena, and wintergreen.
Certain oils are associated with significant toxicity in cats, including wintergreen, sweet birch, citrus oil, pine oils, ylang-ylang, peppermint, cinnamon, pennyroyal, clove oil, eucalyptus, and tea tree.
Another list cautioned against using the following oils in children under seven years old, due to reports of skin irritation, breathing difficulties, uncomfortable skin sensitivity, changes in alertness, or increased blood pressure:
Basil, Bay, Sweet Birch, Camphor Cardamom, Cinnamon (bark or leaf), Citronella, Clove, Cumin, Eucalyptus, Fennel, Garlic, Lemongrass, Oregano, Peppermint, Rosemary, Sage, Tagetes, Tarragon, Thyme, and Wintergreen.
Several sites cautioned against diffusing oils for long periods of time or "all day long" or overnight, as prolonged exposure may cause lung/eye irritation and does not provide additional benefits, compared with intermittent diffusion lasting for thirty minutes or an hour.
Also, be sure to provide proper ventilation. High concentrations of oil in the air can also be irritating, both to people and pets. When diffusing around pets or kids, it is strongly recommended to always allow them to be able to leave the area, so if the oil starts to bother them, they are able to seek fresh air and get away from the diffuser immediately.
Several sites advised against diffusing oils in the bedroom or anywhere that people or pets sleep.
The type of diffuser is also important. Passive diffusers, like reed diffusers, heat diffusers, non-motorized evaporative diffusers, and motorized fan diffusers disperse the volatile oils through the air gradually and in smaller amounts. Active diffusers, like nebulizing diffusers and ultrasonic diffusers emit microdroplets of oil in the air that can land on surfaces (like your bird's feathers) or be inhaled. If the oil lands on your bird, it can be absorbed through bare skin on the face or legs, or ingested while preening.
Undiluted oils applied to the skin can cause skin rashes in some people/animals. Also, essential oils can be absorbed into the body through the skin, leading to systemic adverse effects, similar to ingestion. Likewise, adding undiluted oils to water (for spraying or drinking) can result in direct contact with the undiluted oil, since the oil does not mix into water. To properly dilute oils, you must use a carrier oil, like coconut oil or sunflower oil.
Before using diluted oils topically, apply a small amount as a "test" and wait 24 hours to check for a skin reaction before using a larger amount. Likewise, when diffusing oils, do a short test run before diffusing a new oil for longer periods. Some reactions may take hours or days to develop.
Pay close attention to labeling. Leaf oil is different from Bark oil and Seed oil is different from Flower oil, even when all four oils are derived from the same plant. Likewise, there are various species of plants with the same or similar names but different safety profiles - like cinnamon and eucalyptus. Some species might be safe, while others are not. The labeling might be misleading or too vague to tell the difference between safe and suspect.
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Anyways, if you want to use essential oils on yourself or your pets, be sure to do a lot of research first. Learn about the good and bad properties of the plants you plan to diffuse and use safe diffusion practices. As a general rule, you should you use lower concentrations, lower durations of exposure, good ventilation, and passive diffusion methods only. Avoid sketchy manufacturers and potentially dangerous types of plant oils. Watch out for health claims that sound "too good to be true", like a treatment that miraculously cures cancer or a medicine that works without any side effects or claims to be safe to use at any dose or by any person regardless of health history or age. Many plants do have beneficial medicinal properties, when applied correctly, but too much of a good thing can be dangerous. Many essential oil distributors make exaggerated, unsupported, or misleading health claims. Be careful and use good judgement.
Just as you should be cautious of allowing your parrot to chew on a branch from an unknown tree, you should be cautious of exposing him to concentrated oils derived from botanical sources.
When in doubt ... just don't!