My little pocket dictionary gives the translation as "strange, peculiar, odd, weird, special, extra, or separate." So yeah, strange is clearly the best answer. I'm a very very rusty native speaker and to me unusual still sounds best, and certainly doesn't seem wrong?
Anyway, can't wait for Czech to hit the iPhone app!
I am not sure I completely understand what you are trying to say. You are spelling everything correctly btw.
Stranger in czech is 'cizinec'. It can mean both a stranger and/or a foreigner. The word it relates to is "cizí", which means "somebody else's" or "foreign" but not really strange as in English.
VlastnÍ and zvláštní do not seem to be related in Czech.
Interesting question for me as a Holanďan and here is why: 'vlastni' in Dutch is 'eigen' and 'zvláštní' in Dutch can be translated as: 'eigenaardig' which could be roughly translated as 'to its own', meaning: 'not common'. This helps me keeping the two words apart.
Don't you just love languages :-)