Toddlers are relatively new arrivals on this planet. They are learning about their world through their senses.They are learning about living and non-living things around them. They are still learning words and language to go with these new objects and experiences. To understand a story requires an understanding of language.
When you interact with a toddler, they understand more language than the language they use. A toddler can get the doll for you before they can say, "doll." Their language skills and attention span are limited. They have vocabulary based on development and experience. They may have experiential memories and associations that they don't have words for. Using pictures, and picture books expands their vocabulary. It may give them opportunity to generalize a sensory association to a picture. At this age you are giving children words for things they see, hear, taste, smell, and touch. When you tell a story to a toddler focus on using pictures and sounds and taste and touch. When you do, attach a word.
If you're telling the story of Noah's ark, use a picture or stuffed animals. Name as many things in the picture as you can. Bring a pan of water with a boat. Name ark or boat, water.
Reading and storytelling as a time when a child or small group of children can enjoy your focused attention and snuggle in your lap or sit close gives story a positive association. Turning pages is probably a little like hide & seek. Maybe they will associate the word cat or the cat on Noah's ark with the furry creature at grandmas.
Naaman. Most toddlers know about being sick, getting washed or taking a bath or maybe going swimming.
The surprise element is fun for young children (if you don't scare them). Naman goes under dirty and pops up clean. Use your creativity. (2 dolls or puppets)
Communion. Toddlers have tasted bread, drink and (hopefully) sitting around a table with loved ones.
Because toddlers are learning words, vocabulary, language, use a big picture that tells a story. Don't make it too busy but point out and name the different things in the picture. Use sound and touch and smell. Point to things: Who's that? What's that? Use a of tape sounds. What's that sound?
Most of a toddler's vocabulary involves nouns. Concrete objects and actions. Pick a toddler. Any toddler. What words do they know? Use the word "Jesus", the word "God" as much as you want, not because it's concrete but I'd put it in the category of learning "Mommy loves you"
I was talking with a professional storyteller the other day. She said that most storytellers can tailor their stories for audiences 3 and up. I asked her about pictures with toddlers but she doesn't use props and pictures for her tellings. So that level of storytelling is beyond a toddler - a church sermon.
Pray with toddlers when you tell a Bible story. Think about family or church rituals and patterns of action that send messages to little children. Praying before you eat, asking God's blessing, prayers at night before bed. Advent candles, a creche scene, advent candles and calendars, regularly pulling down that special Bible book to read or tell a story with your toddler nestled in your lap. I think our calling on God, and actions repeated over and over in the lives of toddlers (like prayer) sends a message to toddlers. If you bow your head and pray at every meal. Your toddler will come to expect that and even initiate it. That kind of thing.
Finger plays (though their small motor coordination is still relatively undeveloped), action rhymes (the sounds and actions are upbeat & fun) and simple songs are other ways to tell stories to toddlers. I still remember being little in Sunday School and trying to do "Here's the church, Here's the steeple, Open the doors, See all the people." I remember the pictures in one of the story books and I'm pushing 60.
Noah's ark: Make a boat in the middle of the room (a sheet, chairs, cardboard). Leave stuffed animals all over the room before the kids come in. Pretend to find and bring all the animals into the boat. Eat, sleep. Then take all the animals off the boat and find them homes. How about that! Ok. Herding toddlers is alot like herding cats but try it. You never know. Maybe use a box instead of a sheet. One big enough for everyone to get in. No, not in the water...Send parents to places where there are lots of animal sounds and listen to sounds. (a farm, an animal shelter, a zoo, the woods) Name the sounds!
Doing is how toddlers learn. It gives them opportunity to use their senses and to learn names. Those experiences will give story more meaning as their language skills grow.