My suggestions, based on my limited experience in public speaking, are mostly physical things that help disguise your anxiousness:
- keep any introductions, explanations, banter etc to a mimimum. Prepare and practice a script of sorts for this stuff but make it natural. Knowing everything you have to say well helps so much.
- have something to hold onto/hide behind. Will you have a podium or a table or something?
- Don't read off a piece of paper. Get something heavier to hold (like a journal); it makes shaking less obvious
- Breathe deeply, speak more slowly than you feel naturally inclined to at the time and take brief pauses to gather yourself when necessary. You can end up speaking lightning fast without knowing it, which only makes you sound more nervous.
- keep you body relaxed without tension in you muscles. Physical tension will only add to emotional tension.
- Make sure you look up now and then, keep your head up so people can see you face as you read and perhaps add a few small head movements here and there. This breaks things up and makes you, and what you are saying, more relatable.
- best advice: treat the whole thing as a performance. If you separate yourself from the situation and behave as if you are someone else (or at least an ideal version of yourself) it will make the whole thing easier. You know how liberating it is at costume parties to get into a character? Try to channel that (minus the costume of course). I assume that you are reading a story that isn't a personal, non-fictional experience so an act of sorts won't be inappropriate or disingenuous in this situation. I pretend I am a ENFJ: confident, upbeat, personable, and appropriate.
Finally, have confidence in your stories. You should trust your judgement (and that of those that included you in the event) that they are of a high enough standard to make them worthy of being heard by the public; otherwise why would you have put them out there first place? And if you believe in them, others will too.