You are correct about household chemicals being extremely toxic to birds. Even air fresheners, both aerosol and the plug in type are toxic - they produce fumes and chemicals that can kill a bird quickly.
The carpet powder would be a hazard. Vacuum cleaners do blow out air, and invariably there will be tiny airborne particles of powder that a bird can breathe in. Because these particles will be so tiny as to be invisible, they will remain airborne for some time.
This page has an extensive list of dangerous household goods:
http://www.parrot-and-conure-world.com/non-toxic-for-birds.html
Your safest option would indeed be to remove the birds to another area when cleaning. Once cleaned, air your apartment out for a little while to remove any airborne chemicals.
EDIT: Don't use scented candles either. They also release chemicals that are toxic to birds.
This page has an extensive list lower down of common dangerous household chemicals: http://www.parrot-and-conure-world.com/non-toxic-for-birds.html
Here are some ideas for bird-safe house cleaning:
http://www.eppa.ca/meetings/spring%20cleaning.html
http://www.lineolatedparakeet.net/forums/showthread.php?t=3148
http://www.birdchannel.com/bird-diet-and-health/bird-care/toxic-bird-air.aspx