Strategy Cards are selected during the Strategy Phase (duh) and set the tone for the round to follow. Each card contains an Initiative number, which determines turn order, and an additional ability granted for playing the card. (Most cards actually have both a Primary ability for the person playing the card, as well as a Secondary ability that can be used by the other players for the cost of 1 Strategy Allocation counter.
Playing a Strategy Card is a turn. Therefore, if you use a card, you may not act again until your next turn. After you have played your card, allow the other players to play the Secondary Ability of the card (if it has one), and then flip it over to the side that says 'Inactive'. That card is out for the rest of the round.
There are 8 Strategy cards, numbered 1-8, to be used in each game of Twilight Imperium. However, many of these numbered cards have more than one version, so you can pick and choose which ones you want to include in the game. You should always have an Initiative Number 1, 2, 3, 4, 5, 6, 7, 8, for example, but there is more than one version of most Initiative Numbered card. Some work together better than others. Here is a description of each set:
There are 2 versions of the Initiative 1 card. The number (circled in the left image) represents the turn order. In your game, you will select 1 of these two cards to use (not both!) Whoever selects that card in the Strategy Phase will act first in the following round. Unless, of course, the Naalu are present, as they always go first. It is also worth noting that Initiative (on the left) will not mix well with the Assembly cards as both change ownership of the Speaker Token. So I recommend not using them together. The other ability to take back a command counter is pretty awesome, but I usually use Leadership. Also, notice the symbol circled on the Leadership card (at the bottom). This is the symbol for the Shattered Empire expansion, which introduced this card.
Notice that Leadership is split in half (a top and bottom half). This means it has a Primary and Secondary ability. The person who chooses the card may (usually) only play the Primary. This card lists an exception: the active player may also play the Secondary, if he (or She!, though unlikely in TI) wishes. Then every other player may play the Secondary (but not the Primary).
Diplomacy is perhaps one of the least frequently chosen cards but can be very handy in a pinch if you are expecting an attack that you would like to avoid. Diplomacy II is way better because it lets you prevent an assault while still allowing you to attack your opponent, and also allows the Annexation of empty (non-enemy) planets! Note that such annexation removes any domain counters, and cannot be used on a planet controlled by another player.
There are a lot of these. Most of the 3 Initiative cards involve passing laws, which can be either meaningless or have a huge impact on the game. There is an important difference between the Political and Assembly options in that the Political options don't involve a change in Speaker, and so should be used with the Initiative card. Assembly and Assembly II involve a change in Speaker already, and so should be used with Leadership. Either Political II or Assembly II allow the use of Representatives to vote, which I love. They make voting one of my favorite parts of the game, especially if you have an interesting and controversial law on the table. I circled the Shards of the Throne symbol on Political II-that means it came from the second expansion. Note that there is also an option called Civilization. This if for a special scenario that comes with Shards of the Throne which I have never played. Don't use it for a regular game.
Logistics is basically the same as Leadership, so no need to have them in the same game. Unless you really, really love Command Counters, and don't care so much about building more units. I always use Production in my games.
I have a lot to say about Trade, but I am hungry and so will be brief. I don't care much for Trade, but am torn between Trade II and Trade III. I like the mercenaries you can get with Trade III, but I like the fact that in Trade II you don't get money for your Trade Agreements until the NEXT time Trade II is played. In Trade III, you make Trade agreements and then make the money right away. I don't like that as much because it gives players less incentive to maintain good relations to keep their Trade Agreements together. Trade II allows you better leverage with people who may attack you but know they will lose money if you are trading with them. In Trade III, people just say, 'Hey, we can just make the agreement again next time!" This point may be hard to understand until you have played both Trade II and III. But I usually use Trade III for the Mercenaries.
Both of these are pretty cool. Warfare II comes with a High Alert token (featured right) to signify which fleet gets the attack/movement bonus.
Basically the same except Technology II lets you build tech more quickly, Especially if you are the Jol-Nar. Especially ESPECIALLY if you are the Jol-Nar and have a Trade Agreement with the Hacan, and so can afford the cost of buying 3 techs.
Imperial I and II seem geared toward a very fast game by providing many more opportunities for point scoring. Industry might be good if you are less interested in finishing the game than in giant space battles. I usually use Bureacracy, which offers more opportunities to score points but not to the same rapid pace as the Imperial Cards, which many people seem to feel unbalance the game a little bit.