What does the phrase "Nothing like anything" mean? Literally it doesn't make sense to me and also I do not know its figurative meaning either.
To be nothing like means it is completely different and has nothing in common. Nothing like anything means incomparable; completely different from all other things. This is the literal meaning of the term, no figurative or idiom involved.
There are three examples of nothing like anything in the Corpus of Contemporary American English (COCA):
Here the speaker means the event was completely unlike any event previously experienced in the country.
Here the speaker is referring to some type of adversity that this time has a magnitude never before seen, incomparable to any previous adversity.
Here, whatever it is the speaker is experiencing is unlike any experience she has had in the same environment.
"Nothing like X" is a common phrase that is a more emphatic way of saying "not like X". It means that X has nothing in common with the thing you are comparing it with.
So, "nothing like anything" would be used to say that something is completely unique, and would be more emphatic than "not like anything".
On a general style note, the phrase "nothing like anything" sounds fairly informal/colloquial, so you would probably want to avoid it in situations where that matters.
It is a way of saying that there are no common characteristics.
X is not like Y. (could share some characteristics) X is nothing like Y. (absolutely no common