You have had two problems:
links seems not to want to display accented letters literally, even on a correctly configured system, as Heater already confirmed. I do not know if that can be fixed or not. Just use elinks as RaTTuS suggested on day one.
LC_CTYPE="UTF-8" is an invalid setting (you cannot specify a character encoding without a language and country). It is also unnecessary, so find out where it is being set and get rid of it. LANG=whatever alone is fine.
Other than that it should not matter what locale you choose. Even the default can display the Swedish alphabet.