Hi Thomas Engeroff,
Please make sure of following steps:
1> You need to place whole po and mo file generated from poedit, [ click here for poedit tutorial ] there inside theme folder:
2> Then be sure you can find you translated string for specific string on po files
3> Be sure you are using file with prefix is de_DE
4> Finally select the language from site language section. Go here:
Go to dashboard -> settings -> Genearal -> Site Language [ Duetch ]
Let us know if those steps help you on this. and also we had provided you the reference links on previous reply, please go through all this.
Hope this work for you.