Terrestrial Animals
among the domestic animals only goats, sheep, cow and camel are Halaal (permissible to eat) while flesh of horse, donkey and mule is detestable (Makruh), other than these six animals all domestic animals are forbidden to eat (haraam).
Animals having claws are considered Haraam and hoofed animals are mostly considered Halaal though some are considered as Makruh (unpleasant) such as Horse, *** etc. Birds that flap their wings more and glide less while flying are Halaal and those who glide more and flap their wings less are Haraam.
Birds
Birds like pigeon and all its kind are Halaal.
Bat, peacocks who have webbed feet or birds strong enough which can tear apart animal; or hunting birds, like Charkh (one kind of bird) Eagle, Shaheen, Baashiq (which is also called as Baahsaa) or a weak bird like Vulture or crow and its kind should be avoided. There are others that have been made permissible or forbidden. As a general rule any bird that has not been explicitly forbidden we can apply the following “Birds that flap their wings more and glide less while flying are Halaal and those who glide more and flap their wings less are Haraam.” such as chicken, or turkey.
Aquatic Animals
As regards aquatic animals, only those fishes are Halaal which have scales
Every animal that dies without the proper religious procedure is forbidden. If it has warm blood then it would also be Najis (ritually impure) Islamic Jurisprudence has specified and discussed in detail and prescribed the animals whose flesh is allowed.
more resources on the subject:
al-islam.org/laws/hunting.html#2633