Where are you flying from? Friends have brought in two cats in the cabin without difficulty on AA, however they had to be in the same travel carrier. We bring our dog back and forth in the cabin wth out a problem on Delta. They allow one pet per cabin per flight, so booking can be a problem if there are already pets on board. The pet carrier must fit under the seat with the amimal in the carrier at all times. I am told that total wt of pet and carrier must be under 20 pounds but I am not sure of this. Also the dog/cat must be able to turn completely around when in the carrier.
I have no idea about the birds however.
Hope this helps.
Bob K