DA01's suggestion in his comment would handle some of what you need. If you have Acrobat installed, you should have an active plug-in in IE and/or Firefox that will allow you to save the website as a PDF. At that point you could use PDF2ID to convert the PDF to an InDesign document. PDF2ID does an amazing job of building clean InDesign documents, complete with styles that make sense and formatting intact.
An alternative approach, not necessarily elegant, is to use a utility such as HTTrack to download part or all of the site. Then it's a matter of copy/paste into your DTP application from the actual pages, but you'll be certain not to lose any links or high-resolution version of images that are displayed as thumbnails in the Wiki. This could also work in conjunction with the first approach.
What you're describing isn't a common workflow, so you'll likely have to experiment a bit, but my experience tells me that a combination of PDF and HTTrack will likely get you the product you're looking for. I used HTTrack recently on a blog-to-book project (>600 printed pages in three volumes), so I can attest to that as a workable solution where you want to impose your own styling rather than simply replicate the wiki on paper.