Fun fact: the Greeks believed that birds, usually birds of prey, were bad omens sent by Zeus to indicate bad times ahead. Enzo probably doesn't know this about Greek mythology, but he too fears crows.
Crows aren't an incredibly prevalent omen throughout the book, but they are there, and they do show up right around the time that Eve begins to feel the pain in her brain. So, for Enzo, they serve as nightmare fuel, symbols of bad things to come.
"Sometimes when I have nightmares, I dream of crows. A murder of them. Attacking me ruthlessly, tearing me to shreds. It is the worst" (13.3).
That sounds like a huge understatement, Enzo.
Enzo's fear of crows ties in to his fear of bad things happening in his own life. He can't control crows, and he never chases them. He thinks they're smart. They're also strategic when they attack, especially when they're attacking Denny and Eve's forgotten groceries that were left on the porch. Like all things that are unknown and scary, crows represent whatever hides in the shadows and attacks without warning.
Because Enzo is a dog, it makes sense for him to assign an abstract fear to something real and equally terrible, like crows.
The fact that crows are called "a murder" also doesn't help…