There are 3 basic strategies in the early game:
1. Rapid assault. Wait for a decent-sized army on your capital, then start charging around the map and hope that you are able to capture another player's capital while it's poorly defended.
2. Rapid growth. Focus on capturing territory and neutral cities. Vulnerable to rapid assault, since capturing cities will deplete your forces in the short term and leave your capital vulnerable.
3. Defensive growth. Slower and stealthier capture of territory and neutral cities, where you grow cautiously and focus on surviving rapid assaults. It tends to lose to rapid growth, but win against rapid assault.
So the three strategies have a rock/paper/scissors relationship. If you notice that a particular strategy is popular in the current metagame, you can adjust your own strategy accordingly. In eight-player, you know there will be seven losers.
If you want to be the one winner, you have to get lucky. So it makes sense to lean towards a high-variance strategy like rapid growth or rapid assault.
In the mid and late game, players tend to be overmatched against each other. You'll have just 2 or 3 empires remaining. Usually one empire will be significantly stronger. If you are the weaker empire, your best shot to win is generally to form a massive army with all of your forces, charge into your opponent's territory, and see if you can take their capital during a moment when it's poorly defended. If you are the stronger empire, you know you're going to win by default due to the snowball nature of the game. So the important thing is to defend against the sort of surprise attack I just described. There have only been a few times when I lost from a position of strength, when my weaker opponent managed to outplay me on the basic mechanics of territory and city capture. Areas with a high density of cities are especially valuable to take control of, if you can manage to do it, which tends to be difficult.