I've been playing with the words "eigen" and "eigenartig", as well as "Eigenheit" and "Eigenart" and was trying to figure out what differentiates them, and where some overlap may be. I will start with some examples:
Sie ist sehr eigen, was Musik betrifft.
Dieses Verhalten ist ihm eigen.
Er ist etwas eigen.
Er ist eigenartig.
As far as I understand, these sentences can be translated as
She is very particular as far as music goes.
This behavior is very particular to/characteristic of him.
He is a bit peculiar.
He is peculiar.
You see in my translations that there is an overlap in translations 3 and 4, unless I am wrong in one of them. Is it really the case that "eigen" and "eigenartig" mean the same thing when talking about something strange, or odd?
Second, the reason I didn't simply translate "eigenartig" as strange/odd, was because of the noun "die Eigenart", which does not seem to carry the meaning of being strange or odd, unless I am mistaken. For example, "Das ist eine typische britsche Eigenart" is translated as "That is a typical british characteristic". Is it possible that "Eigenart" can still be used to describe something odd?
Lastly, I am totally lost when trying to get an understanding of "Eigenheit", and where this fits into this big picture.