How do I get weekday and/or name of month from a NSDate variable?

There is no need to manually convert to the Swedish words. iPhone will do it for you. Try this:

NSDateFormatter *dateFormatter = [[NSDateFormatter alloc] init];
dateFormatter.dateFormat = @"yyyyMMdd";
NSDate *date = [dateFormatter dateFromString:@"20111010"];

// set swedish locale
dateFormatter.locale=[[NSLocale alloc] initWithLocaleIdentifier:@"sv_SE"];

dateFormatter.dateFormat=@"MMMM";
NSString *monthString = [[dateFormatter stringFromDate:date] capitalizedString];
NSLog(@"month: %@", monthString);

dateFormatter.dateFormat=@"EEEE";
NSString *dayString = [[dateFormatter stringFromDate:date] capitalizedString];
NSLog(@"day: %@", dayString);

Output:

month: Oktober
day: Måndag