Heh, I have frequently been told that I speak really strangely, to the point of one such person sitting across the room and staring at me intently for several minutes until I asked him what was wrong, and he - sounding almost desperate - insisted I told him where I was from because he could not seem to figure out my dialect/accent. And this is when I speak Danish, mind you; not even other Danes can figure out the way I speak. When it comes to English... this was some years ago, but I once actually had an Englishwoman teach me English, and in one of my first classes with her she actually stopped me in the middle of a sentence to ask me where I had lived besides Denmark, because my accent didn't sound Danish at all. Apparently the way I speak is quite perplexing, which is weird because I'm not doing anything consciously for it to be so.
Curiously I never really applied the accents of people of other nationalities to the languages I already knew, even when having a conversation with such people... though I do have an occasional slip-up when I compose sentences of part-Danish and part-English, accidentally pronouncing a word from one language as though it had been from the other. I have noted that I am quite good at picking up pronounciations when I actually want to, though; when I was learning Spanish it became evident that I rarely had to hear a word more than once to be able to reproduce it with correct pronounciation myself (which was not solely a good thing, due to the way Spanish sentence-structure works that does that almost every word has at least two different ways to be pronounced depending on the context, but I digress).