N2 — outside your level filter

ようがない

ようがないyou ga naiN2neutral

savor + have no way to — there's simply no method left to try

ajiwai you ga nai

have no way to — there's simply no method left to try

meaning: have no way to savor

電話番号でんわばんごうも知しらないから、味あじわいようがないよ。

denwabangou mo shiranai kara, ajiwai you ga nai yo.

I don't even know his phone number, so I just have no way to savor. casual

正直しょうじき、なぜこうなったのか味あじわいようがない。

shoujiki, naze kou natta no ka ajiwai you ga nai.

Honestly, I have no way to savor why this happened. neutral

All examples2

have no way to — you've run out of methods to try

電話番号でんわばんごうも知しらないから、連絡れんらくしようがないよ。
denwabangou mo shiranai kara, renrakushi you ga nai yo.
I don't even know his phone number, so I just have no way to get in touch. casual
正直しょうじき、なぜこうなったのか説明せつめいしようがない。
shoujiki, naze kou natta no ka setsumeishi you ga nai.
Honestly, I have no way to explain why this happened. neutral

ようもないyoumonaialternant
味あじわいようもない
a slightly more literary way to say the same thing (対処たいしょしようもない).

する turns this into しようがない, a separate fixed idiom. That idiom just
means it can't be helped, nothing more.