In some cases, "strange" merely means unfamiliar; not previously known. Example: "When I was in China, everything seemed strange to me." This simply means that Chinese culture was new to me; I hadn't experienced it before. In other cases, "strange" suggests that something or someone is different in a way which is not completely normal. Imagine that a man is walking down the street talking to himself loudly. Maybe you have seen other people do that before, or maybe you haven't. In either case, you might say, "That man seems strange to me." This means he seems odd, peculiar, not normal. "Weird" is similar the second meaning of "strange" that I have described. However, "weird" is used when something seems EXTREMELY different or abnormal. "Weird" is used when something is, or seems, so strange, that it is hard to believe that such things occur in nature.

When you get fairly close synonyms like this, it's a good idea to look at the history of each word to see where the differences come from. Interesting stuff! :) http://etymonline.com/

In my opinion they are interchangeable.

The difference in meaning between "strange" and "weird" is very subtle, if there is any at all. I would say that "weird" is slightly more informal. In truth, I can't think of a situation where substituting one word for the other would change the meaning of the sentence.