[50] To a hidden time, into the age, of the age and into the age of the age

19 And he caught sight of a fig tree by the road and went to it, but he found nothing on it except leaves only, and he said to it: Let no fruit come from you anymore into the age [eivj to.n aivw/na]. And the fig tree withered instantly (Matthew 21). 

55 just as he told to our forefathers, to and to his seed, into the age [eivj to.n aivw/na] (Luke 1). 

29 But he that shall blaspheme against the Ghost hath never forgiveness, but is in danger of eternal damnation: (Mark 3 )
29 However, whoever blasphemes against the holy spirit has no forgiveness forever, but is guilty of everlasting sin. (Mark 3 )
29 who but likely should blaspheme into the spirit the holy, not he is having letting go off into the age, but held in is of everlasting sin. (Mark 3 )
29 oj d an blasfhmhsh eij to pneuma to agion ouk eci afesin eij ton aiwna alla enocoj estai aiwniou amarthmatoj (Mark 3 SCSa)
29 oj d an blasfhmhsh eij to pneuma to agion ouk ecei afesin eij ton aiwna alla enocoj estin aiwniou amarthmatoj (Mark 3 Alex)
29 oj d an blasfhmhsh eij to pneuma to agion ouk ecei afesin eij ton aiwna all enocoj estin aiwniou amarthmatoj (Mark 3 VatB)

32 On this account I say to you, Every sort of sin and blasphemy will be forgiven men, but the blasphemy against the spirit will not be forgiven. 
33 For example, whoever speaks a word against the Son of man, it will be forgiven him; but whoever speaks against the holy spirit, it will not be forgiven him, no, not in this system of things nor in that to come (Matthew 12). 

58 This is the bread that came down from heaven. It is not as when your forefathers ate and yet died. He that feeds on this bread will live into the age [eivj to.n aivw/na] (John 6)

So into the age [eivj to.n aivw/na] means throughout the age. 
Whereas aivwni,oj means literally of the age, which means until some time in that age which means until time indefinite. 

So 'into the age' sets a lower limit of one age and 'of the age' sets an upper limit of one age. 

The meaning of into the age is nicely demonstrated in John 11...

25 said to her: I am the resurrection and the life. He that exercises faith in me, even though he dies, will come to life [the sons of the get a resurrection in the last day, the 1,000 year sabbath of the kingdom];
26 and everyone that is living [judicially], and exercises faith in me will definitely not die into the age [this means do not die to the age, i.e. are not dead for the rest of the age. In other words either they do not die at all, or if they die, they are resurrected at some point during the balance of the age, in order that they are not dead to the rest of the age. This age is the world. They do not die at all because nothing can kill an angelic soul except God. When their human soul expires they just go into their angelic soul]. Do you believe this? (John 11).

and YLT have will definitely not die to the age - which captures the meaning.

And everyone living and believing into Me shall not die to the age, never! Do you believe this? 
YLT and every one who is living and believing in me shall not die -- to the age; believest thou this? (John 11:26).

Then we have into the ages of the ages...

to whom be the glory forever and ever. Amen. 
WHO w-| h` do,xa eivj tou.j aivw/naj tw/n aivw,nwn avmh,n (Galatians 1:5)

Into the ages of the ages means until the end of time or crudely forever and ever.

In the Hebrew things are more simple...

4 has sworn and he will feel no regret: You are a priest to time indefinite ~l'A[l. [literally to a hidden time] According to the manner of ! (Psalm 110).

6 Just as he says also in another place: You are a priest into the age [eivj to.n aivw/na] [i.e. throughout the age] according to the manner of . (Hebrews 5) 
20 where a forerunner has entered in our behalf, , who has become a high priest according to the manner of into the age [eivj to.n aivw/na] [i.e. throughout the age] (Hebrews 6)
17 for in witness it is said: You are a priest into the age [eivj to.n aivw/na] [i.e. throughout the age] according to the manner of (Hebrews 7)

The Hebrew and Chaldean words for 'Time'

~[p instance
t[  time, season (Hebrew)
!d[ year, era, time period (Chaldean)
~lw[ indefinite/hidden time period
d[wm appointed time, season