Woah, I was totally shocked at the one person who responded about Science, Warfare and Card Drafting.
First and foremost, in response to this: "Consequently, if you're playing in a group of unequally skilled card drafters, you should watch what everyone is laying out, make a point of pointing out players who are doing especially well (especially in green), and (however uncouth it may be) offer advice on what not to pass that player", I am totally appalled. There is certainly nothing in the rules that state you can't say anything, but trying to tell other people how to play the game not only makes you seem controlling but also lessens the fun of the game. Save the comments for after the game is complete, and then suggest what things others might have done differently (winning the game might help your cause here). For all you know, you are telling them to burn a card so their opponent doesn't get it, but in reality there is a card there that would net them 10 victory points.
Second, going all military is worth more than 18 points. Depending on how many people are playing, it could be worth up to 24. By getting 18 points, you have also reduced two opponents by 3 points each. Put this in perspective that the majority of the games I have played (with 5 or 6 people who thrive on boardgames and boardgame strategy) winning individuals typically finished with 60 points, this is a quick and easy way to 1/3 of the total points needed. True that you do not know how much you will need to invest into military (which is why I try to wait as much as I can into round 1 to decide), but in a normal game, 4 military cards is enough, which is one of the lowest card-to-victory point ratios in the game. With the exception of some Guilds and Yellow Cards that give victory points for opponents resources, Military is up there.
As for Science, I don't see anyway to not make your strategy obvious. You can get away with two rounds of going for science, but after that, everyone knows. This does not mean that you will necessarily be halted in your strategy, but that coming across those cards then becomes increasingly more difficult.
I do agree for the most part that there isn't any one particular strategy that wins the game. This isn't an overwhelmingly strong strategic game, but it has some elements of making the best decision for yourself at every opportunity.
I've played this game dozens of times at this point, and can honestly say that there are only a few things I have learned.
First, do not bother with cards that can get resources from your opponents for 1 less coin (unless you truly have no other better option). This isn't worth it, as you should be avoiding borrowing resources as much as possible. Choose a resource card over these cards and pay the 2 coins if necessary to get the resource you need in the future. You'll spend less coins this way and have more resources for future cards.
Next, try to diversify your resources. This will give you more flexibility in your card choices as well as give you extra income from the opponents who need to borrow the resource. I'm particularly careful to take a resource card that I see neither of my neighboring opponents have (or their neighbors as well!).
In connection with the diversifying your resources, it is also worth the 1 coin to get the resource card with either two types or two of the same resource on it. Don't waste two actions by getting a free brick and free wood card, when you can spend 1 action and 1 coin for a card that does both. Actions are the most valuable thing you have (you typically only get 18 actions per game, excluding some special circumstances), and given the option, I would pay far more than 1 coin for additional actions.
Finally, do not underestimate the ability to build free cards. This is where science can be extremely helpful. For your first few games, just start to become familiar with them. After you have played enough, pay special attention to them. I can't tell you how many times I could have swept the game if only I had built a Library in the second round. Do not confuse this strategy with only taking cards you can get for free, as you should be taking whatever cards will maximize your score, even if they cost money.
Those are my thoughts anyway.