MySQL and sorting umlauts like Swedish åäö
utf8_general_ci will sort Ö with O and you should use the utf8_swedish_ci instead. That will have the correct sorting order, which (IIRC) is that ÅÄÖ go to the end of the alphabet.
For background info, see 220.127.116.11. Examples of the Effect of Collation
If you want to convert existing tables to a new collation, just use the following:
alter table [table] convert to character set utf8 collate utf8_swedish_ci;