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Often in multi-panel figures a single x or y-axis should hold for multiple panels stacked sideways and/or vertically.
I use IDL to make figures for articles but I do not produce multi-panel figures sharing axes in IDL. Instead I make separate figures, each with full axis annotation, and combine these by multi-panel assembly in latex. The advantage of this approach is that I can so choose the panel layout (e.g., as page-wide horizontal rows or with column-wide vertical stacking) while writing the article, and can do so with figures from coworkers without bothering them.
My latex macros to remove superfluous (identical) axis annotation between adjacent panels and rescale different graphs to the same panel size are given in file cutmultipanel.tex. The figures used in the example in this file sit in this zip file. With these you can try the example yourself.