Differences between "vulgar" and "coarse", "crass", "crude", "rough", "rude", "unrefined" as applied to language
Solution 1:
I looked up each and everyone of their meanings, and they all had meanings of "crude, unrefined", and when I looked up "unrefined" it had the meaning of "crude".
So I looked up "crude", and came up with:
Lacking tact or taste/Lacking concealing elements.
Basically, they all mean the same thing, and that is, just not being tactful, and putting things in an unpleasant way.
In their relation to the third and second senses above, they are all as I said, an antonym of refined, but it does not necessarily mean these words denote "obscenity". They may be offensive, yes, or unpleasant, but "obscenity" includes much worse things like blasphemy, or cursing, or highly derogatory terms, whereas your list of words lean more to being dysphemistic.
Solution 2:
These words simply mean - what they normally mean!!
vulgar -- common, non-elite
coarse -- not detailed (think of a coarse, versus fine, handsaw, for example)
crass -- impolite, unrestrained
crude -- simplistic, uneducated (think of a crudely built object)
rough -- aggressive, overly direct, hurtful to the listener
rude -- using swear words; impolite to the listener
unrefined -- so, not refined! not polished, not edited, not educated; in a more raw state.
When you are using words like these to describe something abstract such as language: think of how the word applies to a physical object. With for example "crude" think of a crudely built say table, rather than a finely-made artisanal table.
By bringing your abstract use of a word, back to the physical use, you can greatly strengthen your language usage.