Quite often I come across this kind of thing:

http://www.youtube.com/watch?v=JpRI49OtteM

Is it my game or is it normal? Those big birds get stuck many times.

define "normal"

Don't most birds live or hang out in trees?

Indeed.

best answer ever

Its either a bug or the devs forgot to clean that one up

It's a script that occurs every time you walk past that location. A flock of birds (if you look up) fly to the taller tree to roost. So that's what they're doing...roosting and making a racket.

I've got that too. The one in the video is across the bridge of Riverwood, directly to the right, right? They're not really big birds, rather multiple birds stuck on each other. Like they say on youtube, it's probably the starting point of that fleeing flock of birds, and supposed to be invisible.

In Morrowind the cliffracers got stuck in trees so I would say that is normal.

And I dare say Morrowind did stuck in trees better than Skyrim. Haha had to say it. Those Morrowind bible thumpers are started to rub off on me.

Birds have to land sometime, I guess. Maybe they just like the tree.