Learn Croatian: Imam posao.

In Croatian, you usually don't need to use pronouns like ja (I) because the verb ending already tells you who is doing the action. The -m at the end of imam clearly means "I have". You would only add ja (Ja imam posao.) if you wanted to emphasize that I have a job, as opposed to someone else.

How do you say "I don't have a job" based on this?

You use nemam, which is the special negative form of imam. In Croatian, the verb imati (to have) merges with the negative word ne to create a single word: nemati (not to have). So, "I don't have a job" is simply Nemam posao.

Why isn't there a word for "a" before posao?

Croatian doesn't have articles like "a", "an", or "the". The word posao can mean "job", "a job", or "the job" depending on the context of the conversation.

What case is the word posao in here?

It is in the accusative case, which is the form used for the direct object—the thing that you have. For inanimate masculine nouns like posao (meaning they are objects or concepts, not living beings), the accusative form looks exactly the same as the basic dictionary form.