Let's say there is a person whose job I know of, but I want to know some details, what he exactly does at it. What is the most common way to ask the question? Does any of the following sentences sound natural at all?
What exactly do you do at your job?
What is your job about?
What is the point of your job?
And by the way, which word is more appropriate in the context: job or work?
All of these sentences sound natural.
In all of these except the first one, "job" is more appropriate. "What exactly do you do at your job?" could also be replaced by "What exactly do you do at work?" but there is no difference between the two.
Although cherryblossom is correct with what she has said, there are reasons why you'd use one rather than the other. It is also countable
Job is a noun only, it is work which you do and are paid for.
Work can be a verb or a noun and is more generic. It doesn't need to refer to your job. It is also uncountable.
You can use these set of facts to work out where you should use job and where to use the word work.
"Where do you work?" - although unlikely - could potentially be answered by someone with their evening volunteering. However, asking "What is your job?" is more specifically asking what they do for a living.
