the craft of storytelling
The first thing is that you have to be mindful of the context (where you're performing and why) and your relationship to the audience. The latter is especially important. The SCA royal bard or the congregational rabbi or the person who leads story hour at the grade school have privileged positions; if you are a visiting bard or a pulpit guest or a substitute teacher, you don't have the same relationship to the audience. They can do things you can't do. They earn that right by dint of assigned role, time, and knowing the people they're standing in front of by name. They have a relationship; you just have an audience. Over time you can build a relationship too, but don't assume you start with one. That's presumptuous and rude.
If you don't have that relationship, one of the things you shouldn't do is to demand audience participation. If you are a visitor, you can request but not demand; heck, even if you're in a privileged position, you should be mindful of being too demanding. If you're expecting audience responses (e.g. to questions you throw into the story) and you aren't getting them, back off. With very few exceptions, you have already received a gift of the audience's time and attention; work with what you're given. A gentle prod or two to see if you can nudge things up a level is fine; persistence beyond that must be in proportion to your relationship with the audience. Push too hard and you'll get labelled as arrogant.
A related area is criticizing the audience. We've all seen performers who ask for an audience response (answer to a question, or response to a greeting, or some sort of refrain) and then say something like "I didn't hear you" or "you can do better than that" or things much pushier. A performer with a good relationship to the audience can do that; I can name several people in the SCA and fandom who can command that level of rapport pretty much all the time. They're among friends who've agreed to play along, and it's part of their known style, and the audience has encouraged them. But if one of them goes somewhere where he doesn't know anyone, I'd expect him to modify his style in this regard.
One way to turn me off immediately -- in an adult setting, regardless of the presence of children -- is to talk down to me for the sake of the kids. If you want to tell stories aimed at children, go to where the children (only) are. If most of your audience is adults, you have to be accessible to them too. Lots of us do not think it's "cute" when you use baby-talk and that special "I'm talking to kids" sing-song style. By the way, the older and/or smarter kids probably won't appreciate it either. There are ways to be accessible to kids without being insulting to adults. Learn them, or choose one group or the other.
Many stories are formulas, with things happening in threes being a common motif. Consider the childhood tale of the three little pigs; when the big bad wolf goes to each house you get the same narrative each time (a lupine demand, a porcine rejection, much huffing and puffing, and, twice, dinner), and only in the last case is the outcome different. There are Chassidic stories where you don't get the variation; you get three events following a formula and then the end of the story comes from the consequences of all three. But either way, you get lots of repetition. A good storyteller can keep the audience engaged, and they may even join you on the quasi-refrains, like "and he huffed and he puffed...". A bad storyteller causes audience members to say "ok, and now we do it again with the wooden house". If your audience doesn't seem to be joining you on the second go-round, maybe you should elide some of the details in the third.
I have been lucky enough to hear some excellent storytellers. Almost none of them are professionals. I suspect that ameteurs are more likely to stay in their communities -- whether those communities are SCA groups, fannish groups, congregations, local clubs, or whatever -- and thus get more of a chance to build the connections that I think are essential. There are certainly pros who can do all of the things I've objected to here -- but one of the things that makes them pros is that they give the illusion of that bond with the audience very quickly. For example, I never had the privilege of meeting Shlomo Carlebach (a"h), but I have the impression that he could walk into a room and appear to connect with everyone there instantly.
I have tried my hand at storytelling a few times, in the SCA and from the bimah. I know I'm not very good and I hope to get better. Naturally, I tell the kinds of stories I want to hear. I hope what I want to hear isn't too far off from the norm.

Re: Re Kids
Mind, I don't know how to be entertaining, simultaneously, to a 5-year-old, a 12-year-old, and an adult, so I don't even try for the 5-year-old; he's welcome to listen and I won't do the egregiously inappropriate material in front of him, but he's not my target audience. I won't risk losing the 12-year-old and the adult by trying to be accessible to the 5-year-old, and I'll do my best to give an accurate impression before people commit to the performance.