I have now tried the Swedish Layout AEKII with Aqua's KeyTest software to identify the issue I was having. It seems that the button left of Z that normally outputs <> symbols functions as the key left of 1, which outputs §½. Clicking on the button left of 1 gives no input. I'm not sure where the issue lies, if it's the adapter that's wired for other layouts, or if it's an OS/driver issue since I'm using Windows 7.
All other keys seem to work fine, it's just that the right CTRL, Shift and so on seem to output the same signals as the left CTRL, Shift keys.
Here are some pics of the keyboard:



