The first is pronounced, "fee-KA," and is usually a noun. The origins of the word "fika" are kind of weird: it's a Swedish "secret language" called fikonspråk (or "fig language"), somewhat like Pig Latin in English. To say a word in this language, you split it after the first vowel, then say "fi" and then the second part and then add the first part and end it with "kon". The Swedish word for coffee is kaffe, which turns to "fi-ffe ka-kon," which got shorted to "fika" over time as a secret code used among teens to go out with friends to a cafe, smoke, and have a coffee and maybe a danish, roll, or small dessert one normally has with coffee. The word is usually a noun, used in the phrase "ta en fika" (take a fika), and means to go out with friends to a cafe, drink coffee, have some small cake or something, and chat. One cannot "ta en fika" alone, unless you have voices in your head you argue with out loud.
Note: do not say "fee-TA," a vulgar word for the vagina.
"Lagom" is a Zen-like word. It means, sort of, "the middle way is best." Not too much, not to little, but the perfect balance of both. A good example is food that is neither bland, nor too spicy, but just the way you like it. Baby bear's porridge, chair, and bed were lagom. Lagom is a very Swedish thing, and it's part of why the Swedes are pretty calm and quiet, but might also explain why they are also heavy drinkers.
Allemansrätt means "Everymans's Right," which is a very complex word having to do with the freedom of the everyday man in Sweden when it comes to nature. Basically, you're allowed to wander anywhere and everywhere in the great outdoors, as long as you don't stay there more than over night, and don't leave any evidence when you leave (trash, mud, etc.). The huge expanses of uninhabited forests around the Nordic villages made this a neccessity only just 100 years ago. Nature wasn't anyone's property, but were seen as a common good to which not only the inhabitants in the nearest village had access, but instead also travelers, who had the right to collect what one need for survival en tour through the sparsely populated country. The tradition dates back to Viking time, or longer, including the right to take grass for horses and timber for reparations of carriages, as regulated in medieval laws. (Today the Rights of Public Access are one of few examples of unwritten laws in the Nordic countries, i.e. there is no law about the rights, but instead about the restrictions.)