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This comes into English as a transcription of the Greek third declension plural. English has several words from that same declension. Any that would retain the original paradigm would be uncommon, technical, and obscure. Some that had that paradigm were "lost" due to misunderstanding and back-formation. And further, that declension had a few different realizations of pluralization depending upon the kind of consonant that ended the nominative singular.

So, other examples of Greek 3rd declension plurals in English are:
agon / agones
hero / heroes (originally heros / heroes) (hero being a back-formation of heroes)
polis / poleis
syringe / syringes (also syrinx / syringes) (syringe being a back-formation of syringes)

The closest example to Erinys / Erinyes is heros / heroes, but English lost that singular form, due to the common use of the word and the odd plural, creating a false singular of hero. Likewise syringe. Still, the original singular word syrinx is used in some technical senses with the plural syringes.

I include syrinx as a good example only if you understand something of the phonetics. The final -s SOUND of the -ks ending (of the x letter) is removed and the -es ending is added, just as in the examples of Erinis / Erinyes and heros / heroes. There is a further transformation of voicing of the unvoiced -k- to a voiced counterpart -g-. Such voicing often occurs when suffixes change the context of an unvoiced consonant. When an unvoiced consonant is found in isolation between two (inherently voiced) vowels, it can assimilate that voicing and change into its voiced counterpart. /syrinks/ > /syrinkes/ > /syringes/