Remember Andy Kaufman's character on Taxi? Latka Gravas. He was from "the old country" and spoke a strange language. There were only a few words that were defined like:
"Yaktahbay" - behind/butt
"Nik nik" - sex
"Ibi da" - "yes" or "that is so"
Most of the language was gibberish, or at least sounded like that. But you could always understand what he (and Carol Kane as Simka) were saying due to their facial/body expressions, intonations, etc.
Try this as an exercise, and do it with a coach, friend, group of friends or at a trusted story circle or guild gathering.
Tell the story in gibberish. "Blah, blah, blah" or whatever. Use your body, face, voice, and anything else you can to convey the meaning of the words, just don't use the words. Jeff Gere from Hawaii has used this exercise with pairs. The pairs tell each other a story, then choose one of the stories to "tell" to the group in gibberish.
Remember that this is an "exercise" so, go "over the top" with your gestures and everything else. You can always pull back later, in a real telling. But in this exercise, be outrageous and have fun!
Then, get feedback from the group. What did they think the story was about? Could they distinguish between different characters? Did they get a sense of the setting? Did they have a sense of time passing? What they tell you about what THEY thought you were saying, doing or conveying will be invaluable!
Oh yeah...one more thing...You might want to think about performing a story this way for an audience! What, you say? Outrageous? Crazy? Can't be done? Donna Washington tells the story of the Three Little Pigs with NO words at all...just sound. And it works!