Let me correct my previous statement. Wordpress by default doesn't allow for usage of Categories with Pages, they're reserved for Posts since posts have no hierarchy to associate them with other posts. Same thing with Tags.
Originally Posted by NSX Prime
That said, you can add Tags and Categories to Pages by adding a few lines of code, shown here.
Now, Wordpress's vision for Pages is that they're associated with each other purely by hierarchy. In your particular situation the 8 main Categories on the current Wiki could just be higher up in the hierarchy. For example:
So if you were to go without Categories your URLs would be somewhat similar to the above. The nice part about this is that you can use somewhat generic functions in page templates that will call "all children" or "all children and sub children" and the hierarchy logic defines what will be displayed. Since you have so many pages of content this will allow you to create a handful of templates to cover thousands of pages.
Some downsides are long URLs, and potentially managing nesting may have a small learning curve. I haven't used MediaWiki so I can't comment on one vs. another, but the Pages listing in the WP Admin is really logical and has a search feature, which comes in handy with large numbers of pages.
NSX2398's comment about DIY is an example where adding Categories and/or Tags may be useful. Do you have a test server set up to play around with?