Is "peculiar" completely interchangeable with "strange"?
Peculiar can be used as a synonym for strange. However, peculiar originally has the meaning "particular to a given place or time; unique", and it is sometimes used that way today. And the connotations of the words still differ: strange carries a slight hint of disapproval, while peculiar suggests curiosity and uniqueness more than abnormality.
In my experience there is a slight connotational difference.
Both words refer to something that is unfamiliar to the observer. However, each word implies a slightly different reaction to the unfamiliar object or person. Peculiar tends to imply that the unfamiliar object draws interest and further scrutiny. Conversely a strange object inspires unease or possibly repulsion.
In essence, peculiar means unfamiliar in a good way, and strange means unfamiliar in a bad way.
Let's see what Oxford has to say on this one. Here are the links: Strange, and Peculiar.
Strange conveys the notion of unfamiliarity or oddity.
Peculiar on the other hand signifies particular, special, or abnormal (anything that deviates from the normal or the expected). The etymology of this word is noteworthy. Its meaning as strange is dated later (17th cent.) by the dictionary.