"since ages" or "for ages"?

Solution 1:

There are two different patterns mixing here: "I haven't seen you since last year" and "I haven't seen you for ages"

As evidenced by work in Conversation Analysis, people actually break their own line of thought quite a lot, so it's not uncommon for people to switch wordings mid-stream.

A novel writer might express it like so: "I haven't seen you since ... ages", to highlight the supposed realization by the speaker that "I don't know when I last saw her, so I can't finish this sentence." But in real speech, people do this kind of switching without skipping a beat.

Solution 2:

Since ages is most unusual. There are no records for it in the British National Corpus and only two in the Corpus of Contemporary American English.

Where did you see or hear it? Was it produced by a native speaker?

Solution 3:

I think the correct phrase is for here. Although since could be used colloquially but it'd not be the correct way. Since is usually used when it refers to an exact or precise point in time. Ages is not an exact point in time. Here is an example.

I haven't seen you since last year.