I know only a few,like semantic level to approach its very meaning, the morphology level to understand how single words are build, syntax level to understand the inner structure of sentences. I would like to understand the whole picture about those levels, which do exist and what is their unique approaches.
It all depends on what sort of questions you want to ask about language.
One way to divide up language is by breaking it into its constituent compositional parts.
- Phonetics - studies the physical speech signal. Sound is interpreted in the brain, which leads us to:
- Phonology - studies the how speech signals are perceived, as well as mental categorization of sounds. These conceptual sound categories may combine to form morphemes, which leads us to:
- Morphology - the study of the smallest units of meaning (e.g. "book"+"-s"="books"). Morphemes may combine to form words, and those words combine leading us to...
- Syntax - the study of "sentence level" structure--how words combine to form phrases, and those phrases combine to form sentences. Of course, words and phrases just so happen to have meaning, this leads us to...
- Semantics - the study of meaning, both at the lexical and phrasal level. But of course one word may have slightly different meanings in different contexts, which brings us to:
- Pragmatics - the study of meaning in context.
Parallel to these levels are disciplines like: psycholinguistics, cognitive linguistics, neurolinguistics, linguistic anthropology, computational linguistics, and speech-language pathology. (This list is by no means comprehensive!). These disciplines will use linguistic theory to answer specific questions. For example, a neurolinguist may use popular theories in phonetics and phonology as a framework to answer questions about phonological processes and their neurological realization in the brain.
Now, to complicate things further--every single one of these levels of analysis have competing theories WITHIN them, and listing them all would be far beyond me. So to answer your question: tons!
The levels you refer to seem to be dimensions of language rather than levels. The different dimensions interfere almost all the time. The same string of words (syntax) pronounced with different intonations (phonetics/prosody) can have very different meanings (semantics).
To cite some other dimensions: sociolinguistics, psycholinguistics, diachrony, neurolinguistics, language acquisition studies, ...
See Linguistics (Wikipedia) for more