Around this age, their brains are developing by leaps and bounds, as is their imagination, their understanding of words like "afraid", and so many other complicated intangible concepts.
My dd developed a sudden fear of a little blue elephant that was part of a bath set (I think it was a cute little Noah's Ark toy). She loved the toy boat and all the animals but one day at bath time the elephant made her scream to the point where bath time was misery. And there were no elephant encounters or anything else. She was about the same age your son is at the time.
Don't try to work on his developing a tolerance for owls, or on getting rid of that fear. It's really not about owls. My dd's problem was really not about blue elephants. It's about learning to feel safe. So you can read books about owls till you're hoarse, or take him to see owls at the zoo, but that's not the issue. What his brain did was develop that fear instinct, and it happened to be when he saw an owl. So now, work on a secure feeling, and the power he can learn to develop. He can have a little flashlight near his bed that he can turn on and off by himself (a child safe one). He can pick out a nightlight that he likes (take him to a big department store and let him choose), and he can be the one in charge of turning it on at night and off in the morning. You can spray a soft cloth with a little tiny bit of perfume or a soothing scent like vanilla extract, and you can put the cloth under his pillow so he can smell it when he feels anxious (use the scent very sparingly, and make the cloth soft like silk or something nice to touch). And most of all, don't talk about fear, or owls. Talk instead about how mom (and any other parent or adult who lives in the home) always make sure the family is safe, how you're happy to lie down at night and relax, and continue with a nice bedtime routine. Don't overdo it. 3 stories, 5 songs and a lot of prayers actually might be providing him with too much time to think. He might be picking up on the fact that you're trying to put off the scary time. Relax, create a soothing routine, and show no fear or hesitation when you say good night. Leave the door open a little if necessary.
This phase will pass!