Is there a difference between the phrase
I have no clue...
I haven't a clue...
as well as
I am clueless...
For instance if someone said:
What is wrong with this?
Which of these could be used to answer?
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I'm not a fan of Ngrams, so my answer is based on personal opinion and experience.
Although I suppose that the three phrases would be perfectly understood in context, if I were to use one of them I'd go for the first one (I have no clue) or for a modified version of the second (I don't have a clue or I haven't got a clue).
I wouldn't use the second phrase as it is because in negative sentences the verb have is normally used either in conjunction with got, thus being an auxiliary, or preceded by "don't"/"doesn't"/"didn't" as any other verb.
As for clueless, OALD states that it is an informal, disapproving adjective which means "very stupid; not able to understand or do something", which is a deviation from the meaning of the previous sentences.
As I understand it, all of those three are suitable answers.
I have no clue and I haven't a clue have the same meaning, but I haven't a clue seems to be more used according to this Ngram (blue line = I have no clue, red line = I haven't a clue - which Google changes to I have not a clue).
I am clueless will probably be understood by most people, even though clueless has some negative conotations of stupidity.