When an opponent casts a spell, if Veil of Birds is an enchantment, Veil of Birds becomes a 1/1 Bird creature with flying.
A noncreature permanent that turns into a creature can attack, and its {T} abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn’t matter how long the permanent has been a creature.
It changes into a creature even if the spell is countered.
It triggers when the spell is cast, which means it becomes a creature before that spell resolves.
When it turns into a creature, it is no longer an enchantment.