How very sad. I'm so sorry for your loss. It's really hard to take sometimes.
Hard as it is, a necropsy (by an avian vet) on one of the birds should be done to determine the cause of death, since you have other birds in the cage with them. It's unusual for 3 to die overnight.
Many household products are toxic to birds. The most publicized are teflon cookware, scented candles, and spray cans (lysol, etc.). The link below will take you to a website with more products listed.
Had the birds' activity level changed yesterday? Sometimes a subtle change in that is a clue to something being wrong. However, birds are experts at hiding their illness until they're desperately ill.
How old were the birds? Finches generally do not have a long life span, although some live to a ripe old age. Most live from 5 to 7 years.
Sorry I can't be more specific. If you do have necropsy done, please let us know the results. Again I'm sorry for your loss. Please let me know their names and I'll add them to my Webpage.
http://home.earthlink.net/~canarymom/finches.htm
>>My boyfriend and I woke up this morning and all three of our male zebra finches were dead. The mom and daughter (was a mating pair and their three babies 2 male 1 female) Were crying their little hearts out. We had their blanket over their cage. closed the windows when the sun went down. It's AZ so it doesn't get too cold. What happened. I was reading on one website where the males just up and die for no reason some times. Is this what happened?
Safety Education
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Canarymom
Finches: Melanie, Fritz, Casey, Sandi, Bunkie, and Sarah
Canary: Paulie
Budgies: Sammy, Curaco, and Pablo
Cockatiels: Elmo, Andy, Cleo, and Marley
And
My Rainbow Bridge Flock who are now singing in that other World