What is the radical difference between ‘this’ and ‘a’ when telling a story?

Solution 1:

There is a big difference in connotation between a and this with regards to storytelling. It wouldn't do to simply replace all of the occurrences of one with the other; unfortunately, the subtleties are hard to pin down.

So there was this guy...

This focuses a stronger attachment to this particular guy. The story isn't about any ol' guy; the guy itself is a critical piece of the story.

So there was a guy...

A reduces emphasis on the particulars of the guy. The particular guy in the story isn't that interesting or important; the important stuff comes afterward.

Cedric did this weird thing...

The weird thing is, again, critical. Specifically, the weirdness of the thing is probably what switches the usages from a to this. Cedric doing this thing means that it was that particular thing that caused the events.

Cedric did a weird thing...

At this point, attention is typically shifting off of the weird thing. The events after the weird thing are what really matter.

The carryover from other uses of this may make this easier to see:

I want this car

I want a car

Another way to think of it is to replace this with this particular:

Cedric did this particular weird thing...

And that Fleur girl tried this particular sort of charm...

All of that being said, the everyday use of this usage tends to overplay, and therefore defeat, its purpose:

So this guys does this thing where he wants into this bar and gets this drink that has this color and he drinks it this way.

By signaling that nearly everything is important, nothing actually is. I actually consider the last use in your example to fall prey to this overuse:

... and this great jet of flame shot out...

There isn't actually anything interesting about the great jet of flame; the interesting part of that sentence is the skirt catching fire. The more you use it, the less meaningful it becomes. Use it too much and you probably delve into Buffy Speak.

Solution 2:

I think that the word emphatic was poorly chosen. The intention is to give your story a sense of immediacy; suddenly it's not about people or objects in the abstract, but (nearly) concrete individuals, e.g. not just

"Cedric did a weird thing (that I'm going to describe to you)"

but

"Cedric did this weird thing (that you are witnessing as well at the same time as me because I am relating the story as though it is happening right now)."

(thanks to @Kit.)

Of course, it doesn't really work; the story doesn't really become any more real to your listener, and if you over-indulge in this technique the constant repetition of "this" starts to be a bit annoying. For this reason, most people (of my US English-speaking acquaintance and reading, at least) stop talking this way after high school; writing dialogue that uses this technique is a good way to establish your characters' age. Definitely "informal."