Unaccustomed as I am to public speaking... (Though the average courtroom is very different from an event where people are expecting to be entertained -- doubly so if they've had to pay to be there!! -- I think there is a crossover of technique as both involve needing to get the audience on-side and not bored rigid!)
Anyhow, I should say that when I made that comment about comedy pieces, I was thinking of stage/screen ie something dramatic, where pratfalls etc can do some of the heavy lifting, not just a written piece read aloud. Though in that regard, I've not been to a live storytelling of the kind you're envisaging, so this might seem a silly question, but is it actually storytelling, or storyreading? To my mind, the two are rather different.
A storyteller needs to have the main parts of the story fixed, but can embellish and embroider as needed, and can use gestures and his/her whole body to help tell the story -- it's a performance more than anything else. (This is very much the advocate in the courtroom -- bullet points to hand, but leeway for the actual words used, using emotion as much as logic to get the story across.) A storyreader is necessarily constrained by the words on the page and in the absence of an autocue will likely have less scope for physicality, so it's harder to generate atmosphere -- also more attention is going to be focussed on the words themselves, which means those words have to be very good indeed if the audience is to be kept engrossed.
In either case, I'd argue the most important thing is to understand how to use one's voice. I've been to book readings and while the authors weren't all as execrable as HB's poets, there was far too often a sameness in the tone and pitch during the reading which made for very boring listening. It's necessary to have some theatricality of presentation, so for instance if there is dialogue, to read the speech slightly differently from the narrative text, and to try and distinguish between speakers -- there's no need to try for different accents, but eg a deeper or harsher tone as opposed to a lighter, brighter one.
The other issue I've encountered at book readings is that the wrong piece is chosen and the extract isn't interesting and/or dramatic enough to hold the audience. That's not such a problem with short stories, but I'd still advise that you choose well -- have something with a cracking beginning, in order that the listeners are with you from the start.
I'd argue against Kerry's suggestion of looking above the audience's head. That would be perfect for a singer, but as a storyteller/reader you will need to engage more with your audience. You have to know if they're with you or they're getting fidgetty from boredom, and the best way for that is to keep looking at them so you can see how they're reacting. Don't look at one person, but have your gaze range over them all -- move your head, rather than swivel your eyes! -- drawing everyone into your ambit. Storytelling/reading is a two-way process between you and the audience -- good storytellers (like good comedians/actors/lawyers) will feed off those who are listening to them.
And though I've not been to any story/poem readings, over the years I've been to countless talks and lectures, both scripted and unscripted. The best have invariably been the latter, because the speaker knows his/her subject inside out and without having to read every word s/he has been able to inject real passion into the subject. (On one occasion we heard four speakers, one after the other, and the only one who was any good was a novelist who roamed back and forth across the dias as she spoke without notes. The others -- all university lecturers -- stuck to the lectern and their script and were boring, notwithstanding the subject matter. The novelist had learned she had to enthuse her audience to keep them listening, so she could sell her books. Seemingly always having a captive audience of students, lecturers/teachers generally don't have to put any effort into being interesting!)
As to practical matters, practise, practise, practise. Speak slowly, but not funereally so; don't mumble into the script or at the ground, look up and speak clearly. Record yourself and listen to what works and what doesn't. Have someone else listen and give feedback on both the story and your performance. If there are words you trip over consistently, re-write! If using a paper script, if your hand is likely to shake through nerves, see if you can rest that arm/wrist against the back of a chair, or put the script on a table, or perhaps write it out in a stiff-backed notebook, so the indivdual pages don't flop over. If you think your legs will give out, see if you can lean back against a table and perch your bum on it to give you support. (And envisaging your audience in the nude doesn't help, it just produces nightmare images on the one hand and giggles on the other!)
Good luck with it! Be sure to report back when it's over!