Hi, going through this book and as usual the grammar terms are not explained so have been using various sources such as renshuu and jgram, however can anyone explain the difference (if any) between the following.

1. ないことはない
2. ないこともない

And also

3. ないではいられない
4. ずにはいられない

Another thing, is knowing the difference needed?
I know previously from N3 book that with most of the chapters that while there are 4-5 grammar points per chapter they tend to have the same general meanings.
For example for the 1&2 above means (it's not that..) and point 3&4 generally mean (can't help but) etc

Between 3 and 4 is basically a formality thing. The -zu negative is a formal written thing (a leftover from classical japanese) where 'zu ni' means 'naide' and 'zu' means 'nai', and various grammar patterns can use either.

For JLPT and similar test purposes you won't get questions that give you two interchangeable answers -- but they do like to ask questions where the context means only one choice is possible, or where the following particle or the verb tense means one answer won't fit.

On 1 vs 2, try the comment in English from matsumomushi in this lang8 post or the answers to this italki question.

thanks for feedback.