If you are awaiting a job offer then the paperwork to complete the hiring process may be waiting for a signature or a final review. If the position is not yet open then you might be waiting for an opening or waiting for something to be complete before they are ready for you such as the completion of a background check. You might also have to wait for you to graduate or complete a certification prior to employment. One way your sentence might make sense is if you are asking for a ride from someone and they are going past the place where you work then "my job is on the way" would say that they could easily drop you off.

No, you can't. It sounds silly. If you've been offered a job you would say: I have a new job. It starts [time]. If you haven't been offered a job, then you say: I don't have a job.