They're synonyms, but "weird" isn't a word that I would use in a school essay. In other words, it's a little more conversational, informal. Teenagers and kids generally use the word "weird" more often than "strange". However, adults do say it, too. If there is any difference between the words "weird" and "strange", it's that "weird" sometimes has a comical or humorous effect attached to it. Odd, weird, strange, unusual -- all of these words convey the same meaning.

They're basically interchangeable synonyms.

Generally, strange can be used to describe someone that is a foreigner or when someone does things in a different manner than other people. The word weird can be used the same way; except when you are talking about something that is supernatural, or that is related to witchcraft, or is mysterious.