A note on "essential oils"...As Noodles and many others have already mentioned, ANYTHING that emits scents into the air can irritate the respiratory system of a bird, including their air sacs, and cause them to have breathing issues. So there are really different issues with "scents" being emitted into the air around your birds, first is whether or not the fumes/smoke is actually toxic/poisonous to birds, and then second is whether or not it's going to irritate their respiratory system and cause them breathing issues even though they aren't actually poisonous/toxic and going to kill them...at least not instantly...
There are so many different Essential Oils out there that it is very difficult to be able to know which ones are actually toxic/poisonous to your birds and which ones are not. And I'm not just talking about the type of Essential Oil, meaning it's scent/source, but also the brand that you buy and what the manufacturer's process is when extracting/filtering/bottling their Oils. There are an awful lot of cheap Essential Oil brands out there, and are what I like to call "dirty" Essential Oils, meaning that they are not simply the natural extract taken from a certain plant.
Generally speaking, the purer an Essential Oil is, the more expensive it's going to be. And you always need to read the entire label, especially the ingredients list, to make sure that there aren't a bunch of nasty chemicals and preservatives added to it. The fewer the ingredients in an Essential Oil, the better.
****Now the issue of choosing an Essential Oil that is not immediately toxic/poisonous to your bird, as there are MANY that are extremely toxic to not only birds, but to us as well. For example, I love the smell of diffused Tea Tree Oil, but it's extremely toxic to birds when they breath it in. So you always have to do your research and make a list of the safe Essential Oils versus the toxic/poisonous Essential Oils; a lot of this should be common sense as well, and you need to use your head, because even though a particular Essential Oil is "safe" or rather "non-toxic/poisonous" to birds, that doesn't mean that it's not going to cause your bird irritation in it's respiratory tract. Don't ever burn/diffuse any Essential Oil that is very strong or noxious to you, because it's going to be much, much stronger to your birds. And once again, unfortunately, the safest way to diffuse Essential Oils is to not do it in the first place.
Not everything "natural" is safe for our birds, and unfortunately, when it comes to odors/scents/fumes/smoke, they pretty much ALL are in some way harmful to our birds.