As you got your data from OSM i assume you can also get the data in .osm.bz2 format. I also assume you are using linux.
Then find out what the bounding box is that you want to work with. If you go to www.openstreetmap.nl. Go to the map and then zoom to Sweden the lat,lon is shown in the top right of your screen. Let's say the bouding box is top=54.0, bottom=53.0, left=6.0, right=7.0 (yes i am aware this is not Sweden).
Install osmosis and bzip2 with the package manager.
Then do the following command to get a dataset that only consists out of the area you are interested in:
sudo bzcat sweden.osm.bz2 | osmosis --read-xml enableDateParsing=no file=- --bounding-box top=54.0 left=6.0 bottom=53.0 right=7.0 --write-xml file=-| sudo bzip2 > part_of_sweden_you_are_interested_in.osm.bz2
Then uncompress your file:
bzcat part_of_sweden_you_are_interested_in.osm.bz2 > part_of_sweden_you_are_interested_in.osm
I assume you want to route over your network, so you have to install pgrouting and osm2pgrouting. There are several guides on the internet how to do this as i don't know your specific OS and version.
You already have a postgresql database with postgis extension. Make sure it also has the pgrouting extension. After that do:
osm2pgrouting -file part_of_sweden_you_are_interested_in.osm -conf mapconfig.xml -dbname your_db -user your_user -clean -host localhost -passwd your_pwd
Now you not only have a database with just the area you are interested in, but also routing tools to work with this data.