Why haven't birds been irradiated/extinct? I think the nuclear explosions would of at least fried them. For example; by one of the SATCOM Array's (The one that fires missiles) you can see a bunch of birds circling a specific area. If they were irradiated, why not include random encounters where giant pigeons just swoop down and spit acid or something at you.

Also: Just a random thought, are centaurs like 5 humans put together or something? Because that's what they look like.. lol

the birds? i guess theyre just there for the heck of it, or it might be too hard for the engine to handle flying birds.(much different from bloatflies, unless we had irradiated hummingbirds)
on the topic of radiation, when a nuke goes off, it scatters almost microscopic particles of dust, metal, and dirt, they go into the air, and have a bit of radiation. this is actually the fallout. birds could probably get quite a bit of the fallout since they're in the air. but also take this into mind, the nuke that went off at hiroshima flattened 5 square miles. flattened it, and if most of the birds are around those cities, they'll be exterminated. then when fallout gets picked up by the wind and carried, it may still fall on the birds. since the capital wasteland only got a few hits from nukes(not much nukes except for maybe the one at megaton, if a nuke hit the town of DC directly, it would be gone...completely.) i'd imagine some had lived, but the searing heat that immediately set everything on fire would kill most of them, and most of the trees theyve been in.

about the centaurs, in fallout 1 and 2 i believe they were experiments by the super mutants on the west coast, how they got over to the east could probably have been where the mutants were driven east..

Centaurs, I believe, are a selection of various animals thrown together in an FEV vat, and see what happens. There might be humans in there too.

Fallout 3 didn't adress the lore of birds, and I suspect they were used more for the cinematic appearance of 'birds circling on the horizon'... They also tend to be over human settlements and so may simply represent a further attempt by Bethesda's developers to use a 'landmark' system. Although I rarely needed visual landmarks in the game, discussion prior to the games release, and the ever present references in the official strat guide, indicate this was important to someone. That being said, the cliff racers in Morrowind were pretty universally hated, so I wouldn't expect them to use a similar critter until the flight mechanic is less annoying.

As for birds in a Fallout universe; considering that we never see them up close in game, maybe they are mutated...
After playing Red Dead Redemption, I wouldn't mind seeing birds like glowing vultures feeding on carrion, or four-winged seagulls swooping over bodies of water.

Are there any canonical references to avian life in the universe?

Vultures and Falcons... They are definitely in the skies.

There is birdsong heard in Vault city in FO2, but its inclear as to whether that is actual birds, or recordings.

^^
Nice find.
I was just playing FO2 again and noticed that, myself.
You'd havta think that the recordings are a pretty reasonable assumption.