There are two questions here.
1. Are you trying to get your messages' spelling checked? That's done by Aspell (as opposed to spell checking in LibreOffice, which is done by Hunspell), so you need to make sure you have the Danish dictionary. See
http://aspell.net/man-html/index.html
An alternative may be possible. In some distros, programs use Aspell via Enchant and Enchant can be told to use Hunspell. This is done by creating
~/.enchant/myspell/
or
/usr/share/enchant/myspell/
and putting in either copies of (or links to) the Hunspell/OpenOffice/LibreOffice .dic and .aff files.
2. Are you trying to get Claws to show its messages and menus in Danish? I've just looked in /usr/share/locale/da/LC_MESSAGES and my Claws (3.7.8) doesn't have a messages file for Danish. It yours doesn't either, then there's nothing you can do about that.
As for the environment variable, type in a terminal
echo $LANG
I get en_GB.utf8, so you should get da_DK.utf8
If you don't, you can put
export LANG=da_DK.utf8
in ~/.bashrc
I think that's a solution, but it's not something I've ever needed to do and Gentoo-based systems are a bit of a mystery to me!