The first thing I would recommend is a very awesome twist on the idea of a free album. Sofia allowed 13 artists from around the world to each remix one song from her 2007 album Street of Dreams, the result being Street of Dreamix, which can be obtained totally free from her website. This album is very similar in spirit to the Nine Inch Nails remix albums, especially since most of those are also now being given away freely (if a little quietly) on the NIN remix site. Some of my favourite tracks on the album are Tobiah's remix of "It's Silly Now", with its 8-bit sound effects, and Libra's remix of "Running Out of You", which is just an awesome song period.
Sofia's last.fm page also plays host to a number of freely available tracks - all you need to do is look for "free download" links. last.fm pages can be quite volatile, with tracks going up and down all the time, so I can't say for sure what you'll see there when you visit, but some of the great songs I've been able to find there are "Ghosts", "Wish" (the original version of one of the songs from Street of Dreams), and the infectiously catchy "Blåa linjen Hem".
Likewise, her iLike page has a number of free downloads available - just look for the "Free MP3" links this time. The real highlight here is a set of 7 live tracks; a little Googling revealed that these are from a recording of an unplugged concert by Swedish radio station P4. These are among my favourite tracks that I have discovered, as Sofia's vocals and songwriting skills both shine brilliantly in the unplugged format. Also of note on the iLike page is a cover of Joni Mitchell's "River", which is done beautifully.
There's a good bit of overlap on each of these sites, but each also has things that you won't find on the others, so if you like what you hear, you'd do well to hit each of these sites and scoop up whatever you can find. Have fun, and happy listening!