Quite often, many of these terms are used to mean the same thing. I will give you a technical answer of certain differences, but please know that many people will not follow these definitions as any native English speaker would accept many of these words as appropriate in a given situation.
Profession vs trade - A professional is an individual who has gone to College and often professional school in order to learn the technical background of a complex job. A tradesperson is someone who has been trained in a particular trade that more often than not uses more physical skill and dexterity. Professionals are doctors, lawyers, accountants, economists, professors, teachers, etc. Tradespeople are carpenters, auto mechanics, electricians, beauticians, waitresses and waiters, etc.
Job and occupation - What someone does to make money. These terms include all professions and trades. Sometimes, people look at the word job as being a more negative word, meaning I am doing something just to make money, I do not like it.
Career - One's life passion. Something you do because you just love to do it and it truly fulfills you. It can often be a job and is most often described as a job. But, a famous American actor, John Travolta, is fond of saying "My job is acting, my career is being a pilot." This means he really loves flying planes but he makes money acting.
Work - A task assigned by yourself or someone else which you feel obligated to complete. A job is a form of work, and the statement "I have to go to work." typically means I have to go to my job. But work can be anything, homework, house work, mental thinking, gardening, etc.
Employment - Multiple meanings depending on the context. However, employment is a noun which means the state of being employed (or having a job). So, "I am seeking employment" means I am looking for a job. What is your employment means what is your job.
Vocation - Your occupation. Sometimes associated with a strong internal feeling that this is what you were meant to do. An avocation is a secondary job or hobby.
It was long, but hope this helps!