Hi Korsav!
Though all these words are meanings of each other, you could use them in different contexts.
enquire - ask
inquiry/enquiry - investigation, examination, exploration, probe, scrutiny
Eg- Consumers frequently enquire about the shelf life of the products sold here.
query - question.
Eg- I have a query to ask my English teacher.
question - query, enquiry, issue, problem, matter, concern, subject, topic
Eg- What was the question?
Eg- The question is, why did you do it?