I know they all mean something is 'difficult to do', 'hard to...' etc but why have three versions? are they used in different grammatical structures or contexts?
You mean ...にくい。...づらい。...がたい。?like the following
I think these two are interchangeable. At least for me, I can’t find semantic difference. “彼の説明は理解しにくい/理解しづらい” Both explains “it is hard for me to understand his explanation.
...がたい is a bit different. “彼の説明は理解しがたい。”
It is incomprehensible for me to understand his explanation. Or, it is unlikely for me understand his explanation.
I think it is strange to use ...がたい for sense verb since they have the word describes hardness of physical property ...がたい.