Sweden's an unstoppable monster at Deity. Since they're far from straightforward I've compiled a few general hints. But to sum it up, Sweden isn't about allying a few select CS as much as allying ALL of them, and faster than anyone else.
1. Happiness is not an issue with Sweden, and so you don't have to rabidly hunt down every last unique luxury and can instead keep to yourself, playing conservatively by riversides without stepping on any toes and growing fat. Consider each great writer a free luxury and time your first four cities accordingly.
2. Science is not an issue with Sweden, with Scholasticism you end up at Babylon levels of science even before universities are up, at which point you should be surpassing them.
3. Faith is not an issue with Sweden, one religious CS gives you more faith than Stonehenge and after medieval gives you more all three Theology wonders put together. This is where your first great person goes, because a religion will give you lots of Great Prophets that you can use to convert three cities and then gift for 90 influence. No, you won't get first pick on any of the beliefs, but it's not like you need extra happiness, culture or faith anyway.
4. Your natural focus on spawning great people will give you lots and lots of Artists which can be used to bulb a nearly infinite Golden Age a la Persia. However, unlike Persia you don't need to go chasing wonders or policies, just get Guilds and you'll eventually end up with a very long golden age. Freedom is a solid choice for Sweden, so if you can wait until then that's great.
5. Keeping out of the lower tech tree gives you a speedy arrival at Banking, which can net you the awesome Forbidden Palace and Rationalism. Alternately you can rush Printing Press for the leaning tower, but it's not a lock and if you miss it you'll be hurting in science. The most important tech is Industrialization. Pay a CS to improve coal and you'll get first pick of ideologies, which even on Deity is an almost guaranteed victory.
6. If everything else fails, Caroleans. Caroleans are notable for two things - They appear alongside Artillery, the "goodbye, strategy" unit when it comes to city siege, and they're the first unit to potentially benefit from Brandenburg Gate's upgrade stack. Although it might be a bit overkill, since they start with March.
In the end, Melee units are best used as walls for your Ranged units, and starting with March makes Caroleans the very best at this. Don't believe me? You can pillage an improvement, move into a favorable terrain and still heal a total of half your maximum health in one turn. Due to 1UPT, before Bombers it's actually fully impossible to kill a Carolean in one turn if you have them in formation. Also due to 1UPT, healing while STILL ADVANCING AND FLOODING THEIR BORDERS WITH TROOPS is more or less unstoppable. Odds are the city will be shelled into nothingness before you've lost any Carloeans.
Non-Russians tend to hold out until Bombers for post-industrial warfare, meaning that you get a very deadly initiative. The only problem with Caroleans is that they don't last forever. Oh wait, they totally do, and they upgrade to 70 str in no-time. Get some Fighters and you're pretty much set for life, people who aim for your Artillery will swiftly find out what five guys with that +50% Siege upgrade does to a poor little 75 def city.
So, world conquest or just get one of those juicy capitals with tons of wonders. The world's your Meatball. Did I mention that city states are absolutely terrifying on Deity? While not much help in taking down a capital, your various allies will eat a huge chunk out of your enemy's armies on every front. Navies are a non-issue. Don't worry too much about losing friendships due to warmongering, at this point you've probably eclipsed everyone else anyway.
7. The Hakkapelitta. Hmm. Well now. I assume they were meant to work as axillary units for the Caroleans, taking out distant threats with their superior speed. Question is, what threats? Caroleans are unstoppable. Even with a great general you're much better just sticking it among the already very quick Caroleans. Even the AI rarely targets them, they're not registered as a threat. Get one and use it to mop a few workers or pillage the enemy's... Iron...? But Cavalry is much better at that and upgrades to landships.
8. Tundra. Just... No. Nobody's forcing you to work those tiles, you'll be using lots of specialists anyway.
9. If you aren't playing Deity, you can just claim Hanging Gardens and declare victory. There are a few beneficial wonders that you're likely to get on Deity though. The Oracle gives you a GSP which stacks later, extra culture, a faster end to tradition and faster entry into patronage. A total no-brainer.
Going that route you might get a shot at the Hagia Sophia too, totally worth it since great prophets are doubly useful for Sweden.
Forbidden Palace is just a bundle of fun, gets you an edge in the diplomacy game (What, Sweden can be used for diplomacy victories? That's absurd!) and alliveates the unhappiness from your tall cities. Since you basically beelined the tech and picked patronage you're very likely to get it.
The best wonder is clearly the Leaning Tower of Stockholm, but getting it is difficult. If nobody has formed the WC yet, you can be a bit unorthodox and bulb your first GS from the universities to get Printing Press before anyone else, granting you the wonder and a complete chokehold on that diplomacy victory you aren't going to get because those are boring. Hey, free great person.
Brandenburg Gate is good since you've been playing Mr. Nice Guy all this time and won't have a great general. Don't worry, you'll be choking on them soon enough, so you can always just gift it later. The extra XP is awesome for everyone else and meh for you, since Caroleans already have the best possible upgrade.
As for which wonders to STEAL, basically anything you can get. Leaning Tower, Forbidden Palace or a well-placed Petra comes to mind. Remember that the usefulness of some wonders peter off while others grow more powerful with time. Picking Machu Pichu before Notre Dame and Temple of Artemis before Stonehenge should be obvious.