ずには居(い)られないCannot help doing something, Cannot resist doing something

These express internal conflict, but from opposite angles. わけにはいかない implies being unable to act due to duty or social constraint, e.g. 断るわけにはいかない 'I just can't refuse.' ずにはいられない expresses an inability to stop oneself from acting, e.g. 笑わずにはいられない 'I couldn't help but laugh.'

ずに has the core meaning of 'without doing', while ずにはいられない is an idiomatic form meaning 'I can't help but (A)'. Compare '宿題をせずに寝た' ('I went to bed without doing my homework'), which describes inaction, to '彼の話に笑わずにはいられなかった' ('I couldn't help but laugh at his story'), which expresses an uncontrollable response.

Both express uncontrollable actions or feelings, but differ in nuance. ずにはいられない is about being compelled to act (lit. 'unable not to act'), e.g. '彼を応援せずにはいられない' ('I can't help but root for him'). てしょうがない emphasizes a state or feeling that overwhelms you, e.g. '暑くてしょうがない' ('It's unbearably hot') or '会いたくてしょうがない' ('I want to see you so much I can't bear it').

These are nearly synonymous expressions that both mean 'can't help but do (A)'. ずにはいられない feels slightly more formal or literary, while ないではいられない is more typical of speech. Compare '笑わずにはいられない' and '笑わないではいられない' (same meaning, but the latter sounds less literary).

Both express uncontrollable actions or feelings, but differ in nuance. ずにはいられない is about being compelled to act (lit. 'unable not to act'), e.g. '彼を応援せずにはいられない' ('I can't help but root for him'). てならない emphasizes a state or feeling that overwhelms you, e.g. '暑くてならない' ('It's unbearably hot') or '会いたくてならない' ('I want to see you so much I can't bear it').

Both express uncontrollable actions or feelings, but differ in tone. ずにはいられない often has a more subjective or emotional feel, e.g. '泣かずにはいられなかった' ('I just couldn't help but cry'). ざるを得ない has a more objective tone and is used to express external necessity or obligation, e.g. '行かざるを得ない' ('I have no choice but to go').

Both imply that something must be done, but differ in the nature of the obligation. ずにはいられない arises from emotional urgency, e.g. '泣かずにはいられなかった' ('I just couldn't help but cry'). ないわけにはいかない often reflects social duty or pressure, e.g. '謝らないわけにはいかない' ('I have to apologize').

Both express uncontrollable actions or feelings, but differ in nuance. ずにはいられない is about being compelled to act (lit. 'unable not to act'), e.g. '彼を応援せずにはいられない' ('I can't help but root for him'). てたまらない emphasizes a state or feeling that overwhelms you, e.g. '暑くてたまらない' ('It's unbearably hot') or '会いたくてたまらない' ('I want to see you so much I can't bear it').