Other artists you shouldn't miss are:

Håkan Hellström

Laleh

Nationalteatern

Nordpolen - Skimret

Hope you enjoy :)

Hej Teby!
It feels like you are thinking of Tomas Ledin? He has freaking amazing lyrics and every swed knows his songs :)

Other artists are
Melissa Horn
Veronica Maggio
Magnus Uggla
Stiftelsen
Patrik Isaksson

I would also throw in a couple of others:

Linnea Henriksson 

Bo Kaspers Orkester 

:-)

Kent. They released their album Isola in both English and Swedish.

If you are interested in folks music you could try listening to: 

Norrlåtar 

Jonas Knutsson & Johan Norberg

Hedningarna 

Kebnekaise 

Euskefeurat

I could also recommend a Swedish/Danish/Australian band that is bordering to bluegrass/country style  even if it's not typically Swedish: 

Basco