The last two are not so much different phrases as they are a simple slurring of the sounds.
However, the first two are in fact more ambiguous. They could mean that she is not going to place of work (e.g., and office) or they could mean that she is not going to work, whether she goes to a work place or not.
If you slur it into "gonna" you are clearly saying she's not going to do any work. If your meaning is that she's not going to her place of work you would pronounce "going" clearly.
Of course, if that is your meaning it's better to avoid the confusion altogether:
She is not going to go to work today. (Or, if you like to slur your words, "She's not gonna go to work today.")
I hope I haven't overly complicated a simple issue!
And yes, this should apply to the affirmative as well as the negative. As for the age issue, I don't know. It may have more to do with level of education. It may have to do with the situation -- or the person with whom you're speaking.
But I'm not gonna go there!*
* An increasingly common expression in the U.S. which means "That's too hot of an issue for me to touch" or "I'll just leave that topic alone."
Student or Learner