Often strategies that work in duels are quite terrible in multiplayer. Something like a red land destruction deck stands no chance at all against multiple opponents since there will never be enough Stone Rains to keep everyone hurting for mana. There are also strategies that are terrible in duels but gain a lot of power in multiplayer. This article will go over some strategies of each type as well as some general multiplayer strategy and deckbuilding advice.

First I would recommend you get familiar with the terminology Anthony Alongi uses to categorize multiplayer cards. I'll paste his descriptions here:

Rattlesnake cards warn off predators and redirect attention
Think of how you react when an opponent plays Thrashing Wumpus and all you have are 1/1 creatures. Chances are, you're heading somewhere else.

Gorilla cards smash the board and gain massive card advantage in one punch
The easiest cards to notice, like Obliterate or Rout

Spider cards surprise opponents into making foolish choices, and gain card advantage by setting traps.
An example here would be Spinal Embrace.

Pigeon cards benefit directly from having more players on the board.
Think of Syphon Soul or Syphon Mind.

Plankton cards allow multiple players to participate, and feel a bit like a feeding ground
Along the lines of Awakening or Wishmonger.

Cockroach cards have persistent, repeatable effects that just keep showing up in the game.
Flood, Masticore, and Genesis are the sorts of cards that drive the rest of the table buggy.

Multiplayer Myths:

I now want to talk about a couple of mistakes people make in their multiplayer strategies.

Look helpless or you will be ganged up on:

One thing I've read in many articles and have seen in forums is the belief that the best multiplayer deck is one that looks helpless for most of the game and then tries to surprise everyone and win suddenly. They say if you look helpless people will ignore you. This is completely false. Let's say you are playing a four player multiplayer game. It is your turn and you have a Diving Griffin that you played last turn. The second player has out a Seal of Fire. Player three has Wall of Air and the fourth player has nothing. Who do you attack? Attacking player 2 will likely cost you your creature and not get any damage through. Clearly not the best option. Attacking player 3 will accomplish nothing as your creature will just bounce off his wall. Of course you will go for the player with nothing out. This goes directly against the belief that people will ignore someone that looks helpless.

The early game isn't important in multiplayer:

This is slightly related to the last point but isn't exactly the same thing. In some groups anyone who attacks during the early turns are looked down upon. While this makes no sense to me and likely doesn't to any of you I've actually seen this in action on Magic Online. In some of the types of multiplayer on there if you don't just spend your first three turns playing things like Llanowar Elves, Wild Growth, and Sakura-Tribe Elder you are some kind of jerk who shouldn't be allowed to play multiplayer. This is especially true in the Emperor format which has the most retarded magic players known to man. Literally 80% of the emperor decks on Magic Online run green. Every single game is exactly the same. The Emperor casts a much mana acceleration as he can on the first turn while the flanks cast Wild Growth and Fertile Ground on the Emperor's lands (actually all on the same land). On turn two the Emperor uses Early Harvest and occasionally Heartbeat of Spring to generate as much mana as he can and casts the biggest New Frontiers he can. On turn three the Emperor uses the insane amount of mana he now has to cast an enormous Weird Harvest (generally for 20+). The flanks then cast all those creatures they found and win the game in one attack phase. This was fun to watch once but when you realize that every single game ever plays out in the exact same fashion it you have to wonder how it can still be fun after the third game. The proof is in the price of Online versions of New Frontiers (which is a crap rare in paper magic). Price of paper New Frontiers = between $0.50 and $1.00. Price of online New Frontiers = between $15.00 and $20.00. A foil one will run you $100. You could get a Mana Drain for that price. That was a bit of a random rant but the point is that the early game is just as important in multiplayer as in a duel. Your multiplayer deck should be capable of being able to fight off some early disruption/beats and hopefully provide some of your own.

Card advantage is not important in multiplayer:

Card advantage in multiplayer in some ways is harder to get than in a duel and in other ways much easier. A card like Concentrate that gives you a few cards wont have quite the effect it has in a duel. That isn't to say that drawing extra cards isn't good but generally a slower but more constant source of extra cards is more helpful in a multiplayer game. On the other side of card advantage is mass removal. This gets even better as with more players you are generally blowing up more stuff. Control decks need more ways of getting card advantage as they can't just trade one-for-one for most of the game and cast a few card drawing spells to stay ahead. There are just too many threats to be able to answer them one at a time. This is the major reason why permission decks get weaker the more players there are. Counterspell only nullifies one threat and you will have neither the mana nor the cards to answer all of them. You want as many of your answers to provide card advantage as possible. This doesn't just mean Wrath of God type effects. Burn that lets you split up the damage like Fire // Ice and Pyrotechnics or reusable removal like Kumano or Tahngarth can often dominate a game. The path to card advantage is more often re-usability rather than just trying to get two-for-ones.

Lifegain is unbeatable in multiplayer:

Just because you gained 64 life off a Congregate doesn't mean the game will go your way. There is practically no limit to the amount of damage the table can deal if they all go after one person. Once that life total gets above 30 you may find yourself with much more attention than you wanted. I've never advocated trying to appear helpless to get a surprise win but there is also going too far the other way and pissing off the entire table. With enough people gunning for you even a 200+ life total wont save you.

Duel strategies that don't work well in multiplayer:

Land Destruction:

Land destruction can be very effective in a duel. These decks seek to keep an opponent from having enough mana for his deck to perform correctly. In multiplayer cards like Stone Rain and Rain of Tears lose their effectiveness as they only effect one person. Sure you may be able to mana screw one person but nothing will stop the other three from killing you. The exception to this is of course mass land removal like Armageddon, Wildfire, and Catastrophe. These however can make quite a few players unhappy as sometimes an Armageddon tends to add at least another hour to the game. Some people like to be home before 3 AM.

Permission:

Permission decks rely on card advantage to win the game. The permission itself is just a one-for-one answer to whatever spell the opponent is casting. It is the card drawing that provides the card advantage these decks need to win. There is no way you could find the mana or space for the amount of card drawing it would require to overcome multiple opponents with one-for-one answers. The deck might work in a three player game but any more than that and you'll do nothing but piss people you can't stop off. This isn't to say Counterspell is worthless in multiplayer. It is still great for stopping a big threat or a board sweeper from ruining your day. It just shouldn't be the focus of the deck.

Combo decks that only kill one person:

Trix was a broken combo deck. However it would be quite crappy in a multiplayer game. Sure it'll get rid of one person but what about the other three? This is true of not just combo decks but also aggro decks that tend to run out of gas shortly after they kill. Cards like Ball Lightning might be amazing in duels but if the majority of your damage comes from temporary sources like that you likely will kill one or two people then have no chance against the rest.

Good multiplayer strategies that don't work in duels:

Giant Dudes:

Multiplayer is a good place to let Timmy free. With so many people the games last long enough to build up the mana necessary to cast all of those 6+ casting spells that would never work in a duel. With a decent mana engine you could even hardcast things like Myojin and Darksteel Colossus. Besides being Timmy is fun. Who doesn't like actually being able to cast something that costs 8 mana.

Rattlesnake Cards:

I'm talking about cards like No Mercy that while aren't very good in a duel will keep opponents from attacking you. Why attack the person who will wipe out your creatures rather than concentrate on the other people until you find that Disenchant? For this reason it is even debatable whether Seal of Fire is better than Lightning Bolt in multiplayer.

Pigeon Cards:

Syphon Mind is a bad card in duels. It is basically just a cantrip discard spell. Four mana to make your opponent discard one card of his choice is not a good deal at all. However, in multiplayer It will provide much more card advantage. With 4 opponents it causes the discard of 4 cards and lets you draw 4. Drawing 4 cards for 4 mana is a good deal and the discard makes it even better. Cards like Blatant Thievery, Lhurgoyf, Multani, Verdant Force, and Congregate also fall into this category.