ようがない / ようもない

1. 1There is no way or method to carry out the action, so it cannot be done in the situation.Ex. 1
2. 2Circumstances outside one's control leave no means of doing the action.Ex. 2
3. 3As ようのない + noun, describes something that cannot be expressed or handled, such as an indescribable feeling.

Neutral in register and common in both conversation and writing. It often expresses frustration or resignation when every possible means seems blocked. Unlike ほかない, which says only one option remains, ようがない says no option exists at all. Unlike わけにはいかない, which is about social or moral constraints, it points to a lack of means.

• べくもないN1「べくもない」attaches to the dictionary form, is written-style, and combines only with a few verbs such as 「望む」「知る」「疑う」「比べる」, meaning that given the situation, something is simply out of the question; 「疑うべくもない」 also means there is no room for doubt whatsoever.
• がたいN3「がたい」 likewise attaches to the masu-stem, but means 'extremely hard to do', often for things psychologically hard to accept like 「信じがたい」, and can also mean objectively difficult to achieve; it leans written-style, while 「ようがない」 means lacking the means to even begin and is stylistically neutral.
• かねるN2「かねる」 does not mean there is no way; it means one is reluctant or unable to do something due to one's position, rules, propriety, or feelings, with a formal and polite tone often used for courteous refusals; 「ようがない」 stresses that there is objectively no way to start, so the two cannot be swapped.
• っこないN2「っこない」 is a subjective assertion that something is 'absolutely impossible / will never happen', colloquial and forceful; 「ようがない」 stresses that there is objectively nothing one can do, is stylistically neutral, and can also describe an extreme degree. Both attach to the masu-stem.
• 〜ほかないN3「ほかない」 means only one option remains and you have no choice but to do it, while 「ようがない」 means there is not even one option and you cannot do it at all, so they cannot be interchanged. 「ほかない」 attaches to the dictionary form and leans written-style; 「ようがない」 attaches to the masu-stem.
• わけにはいかないN3「ようがない」 means something cannot be done because there is objectively no means; 「わけにはいかない」 means one could do it but cannot due to propriety, duty, or circumstances, and attaches to the dictionary form or the ない-form (the latter meaning 'must do'); the two cannot be interchanged.

ようがない says no means or method exists. べくもない is literary for 'out of the question', and がたい says something is hard or rarely achievable (信じがたい, 得がたい機会) without claiming there is no means. かねる is a polite 'unable or unwilling to', っこない is a casual, emphatic denial of possibility, ほかない means there is no choice but to do something, and わけにはいかない means one cannot do something for social or moral reasons.