For my games I usually don't play on a battlemap, and when I do its just a rough map to establish who is where, not down to individual squares. I use our D&D minis to represent everything.
I would say if you wanted to play with that level of tactical precision then you are either going to want to use the Acrylic (or cardboard) tokens instead of minis OR start assembling a custom collection from a bunch of different sources..
Aysle: The easiest, just use D&D minis.
Living Land: Dinosaurs are easy to find, D&D lizardmen can substitute fine for edinos. Not sure where to find primitives, but i'm sure some system has them available.
Nile Empire: Should be easy enough to find 28mm Egyptian themed minis. Call of Cthulhu investigators for normal folk. Early style supers and 30s vehicles (if you want them) may be the biggest challenge.
Cyberpapacy: Adeptes Arbites from 40k are good substitutes for the church police. Cyberpunk minis should be available from various sources.
Orrorsh: Some of the monsters from D&D minis are just fine (werewolves, ghosts, etc...) There are some good Victorian minis here.
Our 28mm Victorian Sci-Fi / Steampunk ranges cover everything you might need for this genre. We've got excellent Steam Tanks, well-known character figures, interesting martians and even some regular historical troops like the Colonial British and Prussians.
Pan Pacifica: It should be no challenge at all to find ninja and mech suit minis.
Tharkold: This is probably going to be the hardest place to find appropriate minis for. While the Russian troops would be easy enough, the horrors of Tharkold are pretty specific and maybe the Terminator miniatures game is the best I could equate to it. Probably will require some customization.
Core Earth/Untransformed: Strangely another of the more difficult sources of minis to find. There just aren't many modern day normal person minis out there that people want for an exciting miniature sculpt. Army and police should be easy enough, but you are going to have to dig for some concepts here.