When the apocalypse ended the availability of crude oil to the surviving Nordics, electricity became the most prevalent form of energy.
The fact that Iceland, the largest and most resourceful community immediately after the Rash, has a virtually limitless supply of geothermal energy and pre-existing power plants making use of it certainly was a major driving force behind the "switch" to electricity.
In the year 90, the fennoscandinavian countries possess one central hydroelectric power plant each. The Norwegian one is near the capital of Aurland; the Swedish one is in Älvdalen, and thus connected to the capital of Mora by a corridor of cleansed land; only Finland has Silent Land blocking the direct connection between the capital, Saimaa, and the location of the plant, at Eno.
There is no indication yet to what extent the post-Rash societies still use land lines, or what they may have replaced them with. The fact that we've seen a train getting a recharge by means of huge jumper cables in the Sveavägen line's terminal at Mora, however, suggests that wireless transfer still isn't a possibility.
On the other hand, it is proven fact (see below) that they possess battery technology far superior to what was available in the pre-Rash days, so distribution of electric power by transporting batteries around might be a viable alternative.
The probably most important use of energy is propulsion of various vehicles, necessitating the energy to be stored on board. This includes even large ships, which obviously go for days, possibly weeks, between recharges, which is not feasible with any kind of battery that was available pre-Rash. (And still out of the reach of alternatives like hydrogen cells.) Even more amazingly, we have yet to see those batteries take up a noticeable amount of space within any of the vehicles using them.
Other uses of electricity include radios and streetlights, like the ones shown in Outer Mora. Nonetheless, all actual devices are said to be very rare and expensive, and in the case of vehicles, typically reserved for use by the military.