My take:
1) Middle Ages. Strategies: Too many to list; insane replayability, phantastic balance; by far the best Conquest for me.
2) Napoloenic. Again, the nice part are the different approaches for the different Civs (see the RBCiv SG thread). Had by far the most fun with Sweden here. This Conquest really managed to convince me the more Civs I played; didn't like it that much the first time.
3) FoR. Fun, fun, fun. Only drawback is that there are essentially only three different Civs: Sassanids, Celts, anyone else. Strategy? Build up. Get the Scrouge. Get some Warlords,

. And, Gobi Bear also supplied us with the Rome version of this...a real challenge. Among the best scenarios I ever played; I really learned a lot here: How to deal with nearly no military, maximum WW, no income. A bit too hard to be fun, though; more for the masochists...but victory is even sweater

.
4) Mesopotamia. Really interesting on Emperor+, when you don't automatically win by Wonders. Nice builder's game on the lower to mid levels, nicely balanced tech tree. And, you can play it in one single session.
5) WW2. China is great, the others are a bit easy, when you know the incompetences of the AI in modern warfare.
6) AoD. Nice concept, but too easy (unless you play the Iros). Strategies? For the Euros: Get some cities around the important resources (e.g. the Gold in Africa is enough, or the Carribean islands). Place several cities around those, have enough cheap units to pick up the treasures. Natives: Slaves, obviously.
7) RoR. A bit too tedious for my taste. Nice tech tree, nice balance, nice Civ flavor. However, the step from being the strongest Civ to eventually reach Domination is a bit too much for my taste. Strategies: Repeatedly reported, nothing to add.
-----
big distance
-----
8) Mesoamerica. Great flavor tree, nice concepts, completely broken balance: Either insanely easy, or insanely difficult; either you grab some wonders and win on autopilot, or the AI comes knocking with Silent Hunters,
9) Sengoku. Unplayable; two of the units are simply broken (Yamabuchis and Ninjas). Pointless above Monarch, the AI will completely kill themselves by pillaging; the AI simply isn't programmed to deal with move 2 ATAR pillagers. The great historical accuracy cannot save this Conquest.