What are the different approaches of the levels of language analysis as introduced in structural linguistics?

I think most people would want to start with phonetics which is the functionally undifferentiated substrate of phonology (to generalize greatly).

Of course, on the other end, you'd also want to include things like the lexicon or semantics and pragmatics (which some people - myself included - would consider to be the same thing). There's also the paralinguistic level (gestures, etc.).

But much more importantly, the whole concept of levels is highly problematic in linguistics. Language does not operate in those straightforward lines. So there are people studying 'morphonology' or the relationship of phonology and syntax.

The fundamental problem is one of disciplinarity. For example, there are people who would consider phonetics to be a 'science' distinct from linguistics. And while it is true that phonetics requires different skill sets, it's not immune from the interests of language as a whole. In the same way, syntacticians have their own approaches and theories that are often quite difficult to grasp for the uninitiated linguists from other disciplines.

The very idea of linguistic levels of distinction can be a useful heuristic but there's also a very strong case for rejecting the notion as reflecting the fundamental nature of language. Look to cognitive / construction grammar and usage-based theories of language for a critique. However, even those people (like myself) who do not believe in 'levels' as the key organizing principle of language, will refer to them as shortcuts when talking about certain areas of description, so it's certainly worth learning more about them.