What is the origin of the clarity of which you write? I did not find the first two websites helpul at all in tracing the English word “eternal” to “aionios”. However, the third site you mention is an excellent source. I looked up the Greek word αἰωνιος (aionios), and found that the perseus site defines the word as “lasting for an age”. You can verify this fact by clicking on the following link:
The word αἰωνιος was used in koine Greek (the Greek spoken from 300 B.C. to 300 A.D.) to refer to anything which is enduring. The word was used by Diodorus Siculus to describe the stone used to build a wall. The word seems to have been used as meaning “lasting” or “durable”.
Josephus in “The Wars of the Jews” book 6, states that Jonathan was condemned to “αἰωνιος” imprisonment. Yet that prison sentence is said to have lasted only three years, certainly not eternally. The word is the adjectival form of the noun αἰων which means “age”.
But the clincher comes from the Homily of the Epistle of Saint Paul to the Ephesians, written by Chrysostum. He wrote that the kingdom of Satan “is αἰωνιος, in other words it will cease with the present αἰων.” So Chrysostum apparently believed that “αἰωνιος” meant exactly the opposite to “eternal”! ---- that it is “ lasting” but in this case also “temporary.”
I don’t think so. The word of choice for eternal is not αἰωνιος but αἰδιος. The latter word is used in the following passage:
Ever since the creation of the world his invisible nature, namely, his eternal (αἰδιος) power and deity, has been clearly perceived in the things that have been made. Romans 1:20 RSV
Actually the Greek word αἰωνιος never means “eternal”; it usually means “lasting”. Sometimes it applies to that which is eternal, but that fact in no way implies that it means “eternal”.
Matthew 25:46 And these [the goats] will go away into lasting punishment, but the righteous [the sheep] into lasting life."
The “lasting punishment” of the goats does not continue indefinitely, but will some day come to an end after the “goats” repent and submit themselves to the lordship of Christ. But the “lasting life” of the sheep will continue forever. However, that “everlasting” aspect is not inherent in the meaning of the word αἰωνιος.