There is a language/cultural barrier between me and my supervisor, what can I do to improve this situation? I am a PhD candidate at a university in Germany. My supervisor, along with all of my colleagues, are German. I am a native English speaker, hired for a position that does not require German. However, I can speak some German, although it is not as good as the English of most of my colleagues.

In the 4 months I've been in this position I can tell that my supervisor and my colleagues don't like socializing in English. They try their best to speak English around me during lunch time, but I can tell that it's really taking all of their energy and effort to string a proper conversation together, to the point that it's really hard for me to understand their English. I encourage them to speak in German because I can understand more than I can speak. But of course I end up not participating in the conversation as much, which I can tell also makes my colleagues uncomfortable. 

Any tips on how I can improve this situation from my end?
It will be much easier for you to learn German to conversational level than all of your co-workers learn English. Even if they are some-what able to talk in English, conversational English is actually pretty tough, whilst German is pretty structured and easy once you know the rules (and the many exceptions ;) )

More importantly, you moved to Germany. Whilst English is expected of all Scientists, there is probably more of an expectation in your lab that you will, eventually, learn German.

Personally, I would tell everyone you are going to German classes on Monday mornings, etc, and that should not only fix this issue, but also give you a positive perception among your co-workers as someone who is a fixer.

Also, speaking from experience as someone who didn't take their own advice when doing a PhD in Germany - if you dumb-down your English for non-native ears, you very quickly find yourself not being able to speak English with natives. Whenever i go back home my parents think I have some kind of brain damage...