How would you explain at what point using "sau-" for emphasis (z.B.: "Das ist saustark!") becomes somewhat offensive or vulgar with some word combinations?
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The aggravating prefix "sau-" is considered as colloquial the most. You would not use it in other than a family or friends setting.
According to Duden it is classified as rather strong ("derb") when used with a negative connotation.
Therefore in most situations I recommend not to use it
It is not so much inappropriate, but it sounds pretty cheap.
"Saustark" and "saugut" are the most common forms to use "Sau-". In some commercial contexts you can hear "saugünstig".
The forms where it isn't appropriate are "saudoof", "saudumm" and other combinations... where it is used to say "dumb like a pig".
I can't think of any word combinations, where "sau-" would be considered vulgar. In some situations you might not use it because of its very informal register.