Your request reminds me of my own journey to become a better storyteller (http://storymin.es/en/2012/04/not-a-story-teller-by-nurture/). One thing that really helped me was to take a creative writing class. There I learned to focus on writing a story in the here and now, using the senses. It helped me to become a better storyteller in conversation as well.
My experience is that you only become better at it through practice. Theorizing in your mind doesn’t work. So why don’t you schedule a regular meeting (perhaps a lunch with colleagues once a month) where you pick a theme (something that evokes emotion, like when is the last time you felt embarrassed (that’s why the falling stories worked really well)) and together focus on telling it like it happened just a few moments ago. Include details what the place looked like, what you could hear, what you felt inside, what the weather was like, what you could smell. Details that matter make a story memorable.
Meeting people like that is way more fun than watching self-promoting white men on youtube 😉 And it gives the social gathering a focus so you don’t have to worry about asking boring questions to get the conversation going. Even introverts can shine 🙂