Most of them are normally used in different registers (styles). For example, the word 'weird' implies the operation of supernatural influences and it is used as 'strange' mainly in informal speech. The word 'odd' has the meaning 'strange' in some fixed phrases, such as 'the odd thing' and 'it is so odd', which are also used mainly in informal speech. In formal writing I would prefer to use the word 'strange' itself or to explain why a particular situation is strange (for example, 'the measured data demonstrate non-physical behaviour').

I try to use dictionaries, as much as I can, written only in the language I am learning now (but not translation dictionaries to my mother language). Also, the origin of the word often helps me a lot.