To put this into perspective, the reason your gas costs so much is that Sweden/Germany/other European countries have incredibly high gas taxes.
The supply of oil and gas is pretty smooth - Nearly every country pays the same price (with some obvious exceptions - islands, etc.) The reason prices vary so much across US States and Euro countries are taxes placed on the government. If the production costs are really $5 a gallon, the expect to pay $12-$13 at the pump, if Sweden decides to level the same amount of gas taxes.
And the reason for high taxes is said to be to compensate for the commercial disbalance. So high taxes wouldn't be needed if gas could be produced locally.
Actually I think that's just the other side of the coin. While most of Europe has recognized that the public is better off levying heavy taxes to discourage expensive imports, Norway levies heavy taxes to allow for greater quantity of expensive exports. The net effect on society in both cases is positive.
Why is cheap gas a good thing? Cars are far less safe than the alternatives, and also generally speaking result in less exercise. So on two different fronts, you have overall more death and injury resulting to society from cheap gas, while more expensive gas pushes people on to safer transit like trains, and encourages people to walk improving overall health. Minimizing time people spend driving in cars is a good thing.
Its a similar case in Canada, even though we produce and export oil, gas price here are usually a dollar more than US gas price because of higher taxes.
I don't have any reliable data other than my own experience. I would guess 10 - 30 km.
Sweden is a sparsly populated country. Compared to Germany, we have a tenth of the population spread over a larger area. Even though Large parts of the north are practically empty, and the population is concentrated to the cities, the difference is noticeable.
To put this into perspective, prices are nearly twice that here in Sweden: http://www.bensinpriser.nu/ and Germany: http://gasoline-germany.com/statistik.phtml
At 14.30 SEK/l, that is 8.80 USD/gallon.