There can be more of them. I have a mod adding more flocks of birds to the game.
I shoot them with arrows, personally. Lightning magic is an instant bolt making it a little too easy.
Personally, I have started carrying a few hawk feathers instead of cure disease potions. They weigh much less, and since Cure Disease is their first effect as ingredients, simply eating a hawk feather will cure any disease.

Edit: Here's a good vid of someone hunting hawks:
http://www.youtube.com/watch?v=7TlaVpLDQVs