However, 'very' can't be used with strong adjectives. We may say "very tired" but we can't say "very exhausted". Now does 'super' go with any kind of adjectives, the strong ones too?
very exhausted vs. super exhausted
very hilarious vs. super hilarious
very essential vs. super essential
very terrified vs. super terrified
Yes, 'super' can be used in this way. It is typical 'inflationary' language; in other words, sometimes 'very' doesn't seem strong enough to people so they use 'super' instead to make it sound more extreme. It is not strictly grammatical, so for that reason you can use it anywhere you like (as it is 'incorrect' in any case). I suggest avoid using it. In your examples: super exhausted sounds like something people would say; super hilarious rather less so; and super essential doesn't sound very likely to me. It's spoken language, so you might hear it with any adjective.
