Not sure about German. However, the word 'konstig' closely resembles the Danish word 'kunstig' which means fake-ish. 'Konst' in Swedish or 'kunst' in Danish means 'art', so kunstig literally resembles art-ish, which I interpret is something that is not quite real but nor unreal. Conclusion: a sort of deviation of any conventional reality (strange, artsy, kunst, konst).
This is just me, and as I am not a native speaker of Swedish, I will still try everything I can do to help. Konstig, in my opinion, sounds like "come stay". When I hear this, I imagine some creepy little girls saying "Come play with us. Come stay". That sounds rather creepy/unusual to me. That helps me like konstig to weird. That only answers the first question. Sorry I can't help you any further.