These terms are basically different levels of the same thing, and often mean exactly the same thing.
Work is the simplest. Work really just means doing some activity to achieve a result or for some specific purpose.
Job is the next level. A job usually means a formal appointment to perform work. This means you have agreed to do some work for some kind of compensation. Normally it is also repeated, or happens many times. You go to work, go home, and go back to work the next day.
Above this you have a career. This normally refers to a job or related jobs which are held for many years with some kind of progression or advancement.
Finally you have a profession. This usually means a kind of job or career which requires formal qualifications. Teaching is a profession. You normally need a lot of formal education to become a teacher yourself.