Whenever he recounts the story of Momotaro, the way he tells the story draws me in completely.
Each time he tells the story of Momotaro, it's like I'm transferred to another world.
I'm mesmerized by the way he can tell the story of Momotaro.
ご質問どうもありがとうございます。
様々な表現があると思いますが、いくつか自然な表現を紹介します。
1. Whenever he recounts the story of Momotaro, the way he tells the story draws me in completely.
to recount = to tell
to draw someone in = 人を引き込む
the way he tells the story = 彼の、ストリーの語り方
2. Each time he tells the story of Momotaro, it's like I'm transferred to another world.
to be transferred to another world= 別世界に移動される
it's like = みたい、のようだ
3. I'm mesmerized by the way he can tell the story of Momotaro.
--to be mesmerized by something/someone = 人または物に魅了される
お好みに合わせて使い分けてみてください。
ご参考にしていただければ幸いです。