Multiplayer is hyper-agressive. If you're not attacking, there's a pretty good chance you're losing.
Human players are unlike AI players, in that they're capable of planning ahead. Thus, even the most agressive human player is still capable of managing a large empire (planning for currency, strategic religion) and maintaining momentum, whereas AI agressive players tend to peter-out picking fights they can't win.
The simplest way to avoid being overrun is to be difficult to find, or inconvenient to attack. This, of course, isn't always an option with various starting positions.
There are generally three key units to multiplayer military: the Axeman, the Catapult, and the Knight.
The Axeman requires exactly one tech (sometimes two), and the top priority of almost any game should be finding bronze, horses, or iron. Plus, you probably want to bronzework to chop. The axeman is efficient, gets good and versitile promotions, and has no foils until crossbowmen, which are quite far away in terms of tech.
After that, the catapult is easily the most important unit. Stacks of units get very huge in multiplayer, and collateral damage can decimate an entire army. Plus, a hundred turns into the game, cities become impossible to take without bombardment. While a player can roam around your lands all he wants, it's not productive unless he's taking your cities; there are other players to worry about, after all. If a player *is* hanging out in your lands, he either doesn't know what he's doing or he's building a catapult army that's on its way. Pray that some other player goes after his homelands before he takes yours.
If you've got ivory, you get to pick up war elephants if you've got no metal or if your metal's vulnerable. It's not great to give your opponent an excuse to build spearmen, but 8 power is pretty solid, even for how expensive they are.
And knights are fast and smashy. After that come grenadiers, after that come cavs, then infantry, then tanks, then planes. Most games don't go that long.
For early growth, be sure to chop trees early, even before mathematics. Remember that early gain is technichally late gain if you can leverage it. Be sure to chop all the forests directly adjacent to your cities, though
One more interesting strategy is to simply settle-near and work tiles that don't require worker-improvement and/or are unpillageable.
-Floodplains generate 3 food 1 gold naturally, but you still can't work them if an enemy camps on them.
-Grassland forests generate 2 food / 1 hammers and plains forest-hills generate 3 hammers. If you have 2 to 4 archers to spare, you can effectively defend these spaces, though that's not exactly a long-term strategy. If you have enough of these forests lying around to work (probably because your workers haven't had a chance to chop them), the enemy might not be able to keep you out of all of them (or may not want to spread himself out).
-If a coastal city is near a freshwater lake, the lightouse will make each of those freshwater tiles grant 3 food and 2 gold (3 gold if you're financial).