よりほかない

Expresses that there is no alternative but to do something: "have no choice but to ~" or "can only ~". It is used when every other option has been ruled out.

Used when circumstances leave only one course of action, often with a sense of resignation (e.g., after stating that funds are short or no other method exists). It is somewhat stiffer than the everyday しかない and fits written or serious contexts. It is often softened with だろう or でしょう.

• 〜ほかないN3「〜ほかない」 has the same meaning and is generally interchangeable. Lacking 「より」, its exclusive tone is slightly weaker; its listed conjugations center on the dictionary form (unlike 「よりほかない」, which also lists the ない form), and it is likewise formal/written in style.
• しかないN3「しかない」 is synonymous with 「よりほかない」 when attached to verbs and interchangeable, but it is neutral in register, common in speech, and also has the variant 「っきゃない」. It can also attach to nouns to mean 'there is only...' (e.g., 「これしかない」), which 「よりほかない」 cannot do.
• ざるを得ないN2「ざるを得ない」 attaches to the ない form minus ない (する→せざる) and is interchangeable when expressing being forced to do something against one's will. It often attaches to 「言う」 and 「認める」 to mean 'cannot help but admit', and can also be used for things one is happy to do, such as 「買わざるを得ない」.
• わけにはいかないN3「わけにはいかない」 with the dictionary form means one cannot do something due to common sense or circumstances; with the ない form it means one cannot avoid doing something out of duty or propriety. Only this latter sense is close to 「よりほかない」, but since 「よりほかない」 means having no other option, the two should not be swapped casually.
• ようがない / ようもないN2「ようがない」 means not even one method exists—there is no way to do it—whereas 「よりほかない」 means this is the only path left, so you go ahead and do it; they are not interchangeable. 「ようがない」 attaches to the ます form minus ます, is neutral in register, and can also express an extreme degree beyond description.
• までだN1「までだ」 with the dictionary form expresses decisively taking a certain measure, without emphasizing that there is no other way; its tone is crisp and 'nothing to lose', it often follows 「ば」 or 「なら」, and it is neutral in register. It also has the usage 「たまでだ」, meaning 'merely... and nothing more'.

〜ほかない has the same meaning, and しかない is its more colloquial equivalent. ざるを得ない stresses being forced against one's will; わけにはいかない means one cannot do something for social or moral reasons; ようがない/ようもない means there is no way to do it at all; までだ expresses resolve to simply do X if nothing else works.