I have heard that the Greek word aiōnios is more literally translated "age-long", the adjective form of aiōn meaning "age". Aiōnios is translated as "eternal" in most bibles. I'm thinking specifically of Matthew 25:46. Were there any other words or phrases in use in Greek at the time that more clearly expressed the concept "eternal" and that the author specifically was not using in this passage?
First, "eternal" is in fact a direct descendent of the Greek word "αἰών" by way of the Latin "aeternus" = "aevum" + "ternus". When you say "eternal", you could also debate on historical grounds whether you are referring to a delimited or unbounded time. Greek is polysemic and "αἰών" is no exception, but in practice, the indefinite sense is quite common for "αἰών" and generally obvious by context. Consider:
(Platon) "ἀνώλεθρον... ἀλλ᾽ οὐκ αἰώνιον" = indestructible but not eternal
Now, are there other ways of expressing infinite time in ancient Greek? Many:
"τὸ αεί" = using the adverb for always as a substantive
"διὰ παντός" = for ever
(Platon) "περὶ τὰ ἀεὶ ὄντα" = concerning the ever being
(Herodotus) "ἔργον χρήσιμον ἐς τὸν πάντα χρόνον" = a work that was useful for all time
(Aristotle) "ὥστ᾽ οὐδὲ τὸ ἀγαθὸν μᾶλλον ἀγαθὸν τῷ ἀίδιον εἶναι" = so therefore the good is no better a good by its being eternal.
(Xenophon) "ἰσήλικος τοῖς ἀειγενέσι θεοῖς" = the same age as the eternal gods
(Aristophanes) "ἀέναοι Νεφέλαι" = the eternal clouds
(Pindar) "λῦσε δὲ Ζεὺς ἄφθιτος Τιτᾶνας" = Zeus eternal freed the Titans
What words existed in Greek to express the concept “eternal”?
Far and away the most common word for "eternal" in the Greek is αἰώνιος. Of the 68 occurrences of "eternal in the (AV), this word accounts for 63 of those instances.
Other Greek words being translated as "eternal" are:
The other two (2) instances of a Greek word being translated as "eternal," are ἀνάθεμα (anathema), which, in both instances equates to being eternally cursed.