We need a pic mate to really be able to comment.
I know that using a cable release is automatically associated with tripod shots, but that tends to go out of the window with bird shots, they just don't sit still long enough.
With longer lenses, what happens is that as you press the shutter, the mirror flies up creating vibration which travels along the lens to the front and then travels back to the camera manifesting itself in blurry images at the sensor. The problem gets worse the longer the lens, but I use long lens technique on a tripod with my 500mm, 100-400L and the 70-200 2.8 - even the 180 macro if I'm shooting birds.
You need to have a hand on top of the lens to damp this vibration and a cable release really isn't necessary for these shots as the shutter speed has to be fast enough to freeze the bird's movement anyway. I'll find you a link to the long lens technique.
What sort of tripod head are you using? A gimbal head makes tracking birds in the viewfinder and keeping that AF spot on the head a whole lot easier. I always use a single AF point and servo AF for continuous focus all the time.