Wastelanders must not be too picky about their food. However, poultry is very healthy. In fact, crow meat can even sharpen your senses, while gull meat makes you more resilient!

At least in this mod. 

You can now loot crows and gulls for delicious meat and process at the cooking station. Because that's just how it works, "Crow Chunks" will boost Perception by 1 and "Radgull Chunks" will improve resistance to Infection & Parasites. 

Please note birds in Fallout 4 aren't NPCs in the traditional sense, meaning that they don't have an inventory. If you kill one, you will not loot their actual bodies, but a container in shape of a lump spawned at their bodies. So there's always a chance you won't be able to find the lootable part if you shot it from a lantern or midair. 

That being said, they are small birds, after all. Gun holes might not leave too much meat to remain.