The bird should always be removed prior to cleaning the oven. I have permanently removed Teflon pans, candles, room and carpet deodorizers. Also, birds must be kept inside protected from the heat and mosquitoes, especially Canaries. Of course, they would enjoy fresh air on the patio while enjoying the day with its owner to watch over him a screened porch would be ideal.
If you keep your Canary in the kitchen, make sure you do not expose the bird to any Teflon pans (Teflon is odorless but can kill) or strong cleaning agents, like oven cleaners or Clorox, ammonia, cigarette smoke, etc. These have proven deadly. Do not use your self-cleaning oven with birds around! A canary friend told me how he lost 121 Gloster canaries to Teflon fumes. He was boiling water in a Teflon pan and forgot to turn it off. When the Teflon overheated, his birds died very quickly. In the old days, coal miners would bring a canary into the mine shaft as a way to check air quality. If the bird suddenly died, the miners left the area as it was too toxic to remain down there. Canaries need clean, fresh air to survive- no scented candles, no cigarette smoke. I cannot emphasize quality air enough.
The more birds you keep, the more dander will build in the room. Dander is the white powder that helps them ward off parasites. Too much dander causes respiratory problems for you and the bird and should be removed each day. You can purchase an air cleaner or make an inexpensive one from a box fan and air filter. I use a $19 box fan in the room with a standard air filter attached to the back. You will need to change the filter or vacuum the filter often. You will be amazed how much dander and other material this inexpensive air filter traps each day. Use more fans if necessary. There are also whole house air filters available to clean the air and also trap dander.