1. 4p and up games are much faster than 2p and 3p games, because in 2p and 3p games there are 4 provinces per player, but only 3 per player in 4+ games. Therefore, in 4+p games, you should a) green earlier than you otherwise would, since you need to get your share of the provinces and you're less worried about stalling out, and b) you should favor strategies that are fast over strategies that deliver megaturns later.
2. The number of green cards changes, but the number of kingdom cards does not. For this reason I tend to shy away from decks that are combo based and need multiples of a single popular card (especially if that card is a village-type), unless the combo is incredibly powerful or there is sufficient trashing, since it's very likely that you'll end up with fewer of the card than you need and you'll have 1-2 piles depleted or near depleted by the time you figure it out.
3. Rush strategies play very differently. Consider Workshop/Gardens. If you're the only one playing this strategy, you'll likely need 4 more turns to empty the Gardens, plus another 3-4 turns to empty the Estates, than you normally would. In a 4p game, you're talking about needing 7 more turns to end the game -- chances are that the game ends on Provinces before you get a chance to do that. The math changes in similar ways for Duke and Silk Road strategies.
4. Opponent strategy is much more important. In a 2p game, if I go Witch and you don't, I'm probably going to win. In a 4p game, if three of us go Witches, the guy who goes Moats has the best chance of winning. This ties in with the previous 2 points -- if you spot a strong strategy that nobody else does, then you're clear to gobble up as many of the key cards as you need; similarly, if someone else is Workshop/Gardening in a 3p game, it's very likely the two of you can 3-pile very early. It helps to know your opponents, but reading their opening and turn 3-4 buys is pretty important.
5. Opponent skill is more important. In a 2p game, if I get to 5 Provinces first (and there are no alternative VP, etc.), chances are good I'm going to win, even if I stall, because I can buy Duchies. In a 3p game, this is also true...unless one of your opponents is absolutely terrible, allowing your other opponent to green later and beat you by getting 6 Provinces (or 7). It's important to have at least a rough idea of each player's deck and whether they'll be buying Provinces anytime soon, and how many you think they'll end up with.
6. Attacks are much more devastating. Torturer with no village in 2p is pretty benign. Cutpurse is pretty weak after the early-game. Saboteur is only worth considering if you can play it consistently. But in multiplayer, a lot of these considerations go away -- if each of your opponents has a Saboteur, that's pretty similar to having a single opponent who can play his every turn. Same goes for Torturer. When you read the board, consider the possibility that each of your opponents will be playing, say, Bureaucrat, and adjust accordingly.