If you want this to exist all on the same page, you can accomplish this without variables.
Let's say you have 3 checkboxes for the 3 switches. You can add cases to the OnClick event of each of them to set the dynamic panels states accordingly. The OnClick on each of the checkboxes would contain the same 8 cases with conditions like
"if check state of MyCheck1 is checked and check state of MyCheck2 is not checked and check state of MyCheck3 is checked"
then add the appropriate actions. Here is an article and video on conditional logic: http://www.axure.com/p202_1.aspx
Once you've defined the cases on one of the checkboxes, you can right click on OnClick and Copy All Cases and then right click on OnClick on the next checkbox and paste all the cases.
You can also consider linking to different pages based on the checkboxes to show the content in the different layouts. This could help keep the pages simpler depending on the dynamic panels.
Also, if you don't need to demonstrate all 8 scenarios dynamically, you could consider making just a couple of them work and then use annotations and less dynamic pages to show / describe the rest of the combinations.