Sweden can be quite a strong civ when played effectively, and I've also found them to be one of the most enjoyable civs, as the provide a variety of opportunities for strategic decision making and unorthodox strategies that simply aren't available to other civs.
Expanding on what others have said about Great Prophets, I've found that Sweden works remarkably well as a religious civ. My early game goal, when playing Sweden, is usually to create a religion that generates as much
as possible. Pilgrimage (+2
per foreign follower city, including city states) is a great founder choice (Papal Primacy- seems like a synergistic choice, but by the time you can make effective use of it your resting influence point won't actually make much difference) and Pagodas and Mosques are amazing if you can get them, as is Divine Inspiration (+2
per world wonder) if your staring terrain and difficulty settings make world wonders a viable option. When you enhance, choose Messiah, which will allow you to buy more great prophets as well as increasing their conversion strength. Once you have this religion founded, spread it as widely as possible, focusing particularly on city states (this will slow your influence decay, as well as potentially fulfilling quests), switching from missionaries to Great Prophets when the former begin to become expensive and gifting your Great Prophets when they have one use remaining. Once they too become prohibitively expensive, you can start stockpiling faith for industrial era Great People. This strategy does depend on founding a religion (probably through a faith generating pantheon, opening honor and gifting your free great general to a religious city state is possible, but delaying your main social policy tree by two policies is a pretty steep cost) and takes a while to get going, but once it does, it will allow you build up a massive empire of allied city states.
Though Sweden itself did not change with the release of BNW, the mechanical changes in this expansion were a massive indirect buff. Splitting Great Artists into three types and tracking each one's cost separately allows you to generate a huge number of great people in a game, to the point where it actually feels too easy to keep allied with every city state on the map. And rather then simply generating resources and contributing to a diplomatic victory, your city state allies will allow you to control the World Congress giving you a wide variety of choices to strengthen your civ or hinder your rivals (be sure to pass World Ideology if you've been using your artists for influence rather than creating great works).
As for Sweden's military focus, it really encourages you to be aware of the global diplomatic situation and to choose your friends and enemies carefully. Picking fights with one or two aggressive civs that have already made lots of enemies (often Atilla, Shaka, Genghis Khan... ) can actually win you a lot of friends, as well as giving you the opportunity to earn great generals and admirals (gifting all but one or two to city states). Hakkapeliittas are something of a niche unit, and I've never found them exceptionally useful, but Caroleans are quite strong, and the fact that they get march without having to build up three promotions in the same category frees you up to take promotions like medic and cover.
The great person bonus from declarations of friendship isn't quite as strong as it sounds at first (since each great person costs more than the previous one, +10%
doesn't actually mean 10% more great people), but it certainly helps, whether you chose to gift the great people or use them yourself. It's also one of only a few civ-specific bonuses to great artist, writer and musician production, so you could play Sweden quite effectively as a cultural civ if you don't gift these great people to city states.
Overall, I think that Sweden is an exceptionally strong civ, second only to the likes of Babylon, Korea and Poland, capable of dominating the diplomatic game in a way that only Greece can rival while also possessing a very a strong late-midgame military, and a UA that can be used to enhance virtually any strategy.