On the sheim, check out the first 2 pages, they were one of the first civs covered. That being said, if you have a different way of playing them than was posted earlier, please tell us about it - thats what this thread is for.
As for the illians, I just checked this thread and can't believe that one hasn't been posted before this - they are definately a fun civ, so I'll work on corecting that.
1. The first thing the illians get is the temples of the hand. Temples of the hand turn every tile within 2 squares (note, thats 2 squares, not the BFC) to ice. This has several benefits. First off, the illians treat all ice as grassland, and every tile in their BFC is ice. Second off, they can settle anywhere. Desert? Turn it to ice. Jungle? Guess what, jungle can't survive on ice - it turns to forest.
2. The second thing that they get is Priests of Winter, which they get at philosophy. They can only get three, but getting them is often enough to win you an early war.
3. The third thing is the worldspell - stasis. This means (on normal), that no one can do anything for 20 turns. There are a number of ways to use this, but which way you choose is up to you - personally, I use it right before declaring war on someone, as it allows me to attack without having to worry about them getting reinforcements.
4. Traits. Aurics traits are defensive and charismatic. However, he can also get aggressive if he beats the amurites to Legatum Frigus (the amurites get a golden age out of it). These traits mean that his units get +10% withdraw, and anywhere between +0 and +30% strength depending upon where they are and whether or not Legatum Frigus has been found. This makes Auric a very good warmonger, and gives him a pretty good reason to use mounted units as well.
5. Unit Lines. You are going to need to go down the metal line in order to get two of your heros. You're going to need to go down the divine line to get 1 of them, and your high priests of winter. You'll need to go down the recon line and the magic line to get Auric (Omniscience requires Commune with Nature, and strength of will or pass through the ether). Basically, to get all your benefits, you'll be all over the place. I suggest the mounted line as a strong basis for your army (defensive + horse archers, 2 upgrades and they have an 80ish% chance of withdrawing from combat). Usually, I use warriors for a while, get priests of winter early, then go for axmen, then adepts (you start with enchantment mana, use it). Once I have them, I'll generally find out if I have horses, and if I do go horsemen-horsearchers next, followed by mages, then champions. Once I have them, then archmages are usually my next priority, followed by high priests of winter, then drifta, and lastly Auric. If you have different preferences however, feel free to go for them - the illians have a great deal of freedom, only being blocked from religions.
6. Heros. Auric gets 3 heros. The first one is his primary, wilboman. Wilboman is a strength 7 hero who comes along at iron working, but otherwise is rather meh. He's nice, but not awsome. The other two are though. The first one is drifta, who is available at divine essence, and requires that you have killed a civ already (hey, do it early, do it often, right?). He is a dragon, magic immune, strength 14+7cold, and makes a great munching machine. Make sure that you escort him early on though, as it really sucks to loose him shortly after building - after he has combat 5/drill 4 etc. though, he can easily just wander off and eat entire civs on his own. The last hero is probably the most important though - Auric Ascended. He requires omnipotence, the draw, and if you get him, you have probably already won the game anyways. Just don't loose him, or you'll lose your traits. Because of his inability to get promotions, he isn't good to use as a regular attacker - what makes him powerful is that his spell can kill. Use him as mobile artillery
7. Ice. There are two ways to get ice mana - you can get 1 from legatum frigus, and 1 from the illian palace. The first spell, slow, removes 1 movement from enemy units nearby - the earliest stack stopper in the game. The second spell, summon ice elemental, summons a strength 2 + 2 cold, +1 ice mana affinity unit - nice to give to your mages, but nothing super special (it would be, but you can only get 2 ice mana...). The important one is Ice 3. Ice 3 is snowfall - the strongest direct damage spell in the game. It does 40% damage, with a maximum of 80%. This spell can be gotten by: 4 archmages, 4 liches, 3 high priests of winter. Because of how strong this is, you can actually afford to run 3 seperate offensive stacks. I like to run one stack with the liches with Auric (liches cast snowfall, auric casts his, all units within 1 square now dead), 1 stack with drifta (usually use archmages here), and 1 stack with my primary army (usually use the high priests here, as they can cast heal and medic 3 is very nice for a stack to have. It makes lategame mopping up VERY easy.
8. Reaching the lategame. Early game, you have no advantages, except stasis, and if you rush it, the priests of winter. Midgame, you can have ice 2 casters, wilbowman, and that is pretty much your only advantages. Lategame is where your power is. Therefore, you need to get to the lategame, preferably before anyone else does. The best ways to do this are to kill your nearest neighbor early (stasis, fast priests of winter, and a big stack work well for this). Then, spend the midgame teching up in peace, and building up your lategame army. Lategame, come out like a storm and drown the world in ice.
9. Economy. Every square can be treated as grassland. This is nice, in that you don't need to worry about food much. However, it is not so nice in that you will be short on hammers, and you don't get any bonus commerce. Therefore, I would try to settle near hills for production, and its your choice on whether to run Aristograrianism, or to try for a cottage economy. You don't really have any bonuses for either one, but aristograrianism will probably work better if you have nearby sources of freshwater. Standard city planning takes place here.
10. Have fun, and don't forget that your job isn't done until the world is buried under at least 3 feet of ice, minimum
Hope this helps.
-Colin