My previous posts were based on what I know about other places - knowing how things work in countries like Germany I was assuming that identity cards issued to foreign nationals would be different from identity cards issued to Swedish citizens, and that they would identity the holder as a non-citizen. National identity cards are valid travel documents anywhere in the EU/EEA (i.e., not just Schengen), and if non-nationals were given the same identity cards as nationals then they would be able to use them to circumvent entry requirements for places such as the UK.
I have now done some research (haven't looked further than Wikipedia) and it seems that I was right - national identity cards "proper" are only available to Swedish citizens; permanent residents are given a different of card known as a certified identification card.
http://en.wikipedia.org/wiki/Identit...ents_in_Sweden
So... unless the OP can get his visa extended before he travels I don't think he will be able to fly Ryanair.