It has been claimed that Armenia was the first nation to officially identify as a Christian nation in 301 AD, but unfortunately I know very little of Armenian religions/mythology that came before this transition.
As an Armenian-American, we were always told that the people of Armenia were pagans/fire-worshippers prior to Christianity (which I suspect is just a catch-all term). Could anyone shed some light on religion in pre-Christian Armenia/Cilicia?
Early pre-Christian Armenia (6th century to 4th century BC) followed a syncretic paganist religion which was a mix of the indigenous Armenian beliefs and Iranian religion. At this time, Armenia was a satrapy within the Achaemenid (Persian) Empire.
There is debate on whether Zoroastranism was the Persian empire's religion at this time, or if it was actually an earlier polytheistic form of Iranian religion. One of the mods here, /u/Daeres, specialises in this if you want more information on it, actually.
This Achaemenid Iranian pantheon was fairly large and notably contained the gods:
If we look at the Armenian pantheon at this time, we see:
It's clear from this that Iranian mythology had transplanted into the Armenian pantheon. Many Armenian names derive from these Iranian deities, in fact the vast majority of Armenian names have an Iranian origin dating from the Achaemenid and Parthian era.
We know nearly nothing of pre-Iranian Armenian mythology as we do not have mentions of the name "Armenia" as a nation before the Achaemenids, so we can only really work with what we have.
"Fire-worshiper" is often a label given to Zoroastrianism, but it is not an accurate one. There was a cult of fire in Zoroastrianism, but it was not a defining aspect of the religion. Because of the Iranian influence on Armenian religion, many Armenians do call it "fire-worshipping", but it would be an inaccurate term.
After the Achaemenid empire was conquered by Alexander the Great, Armenia underwent a bout of Hellenism (Greek culture). Armenian deities were identified with Greek ones (for example, Anahit and Aphrodite). The temple of Garni is an example of a Greco-Roman temple still standing in Armenia.
Until the conversion of Christianity, Armenian religion can ultimately be described as a pagan religion with a elements of indigenous Armenian belief distinguishing it from the dominant Iranian religion that so heavily influenced it.
They do seem to have very generally followed a mix of indigenous beliefs(what those beliefs are are highly uncertain because Armenian ethnogenesis is generally very uncertain) and more widespread Indo-Iranian beliefs including Zoroastrianism. Unfortunately we have very little direct evidence of pre-Christian Armenian history largely because Armenian was unwritten until after the Christian era and archaeological research in Armenia is somewhat limited for this period(most of what I'm aware of is either medieval, Urartian period*, or neolithic) so most of our records are Christian writings and some Greek and Latin authors discussing Armenia. But we can point to certain known practices. We do have references in Khorenatsi claiming that a fire cult and possible a spring/water cult was practiced(both are associated with Zoroastrianism and in addition various spring cults have a history in Anatolia reaching back to the 2nd millennium and extensively crossing ethnic lines). In addition, Khorenatsi does refer to cults of sacred groves which has been taken as evidence of these practices in pre-Christian Armenia. We also know, as Tigranater points out, that by the Sasanian era at least cults existed of Ohrmazd, Mithra, Anahita, and Vergethana/Vaghan. We also know from Greco-Roman texts that at least some Zoroastrian or at least Mazdayasian practices were recognized by Greco-Roman authors in Armenia. We also know that this was hardly an "overlay" because even when Armenian was christianized there do seem to have been at least a substantial number of Zoroastrian loyalist nobles and indeed the revolt of the Mamikonians was based according to Armenian writers on efforts by the Sasanian monarchs to restore Zoroastrian practices with at least some support by other nobles. Anyhow, if you want further reading on this the most comprehensive overview of pre-Christian Armenia is James Russell's Zorostrianism in Armenia, although it is probably in at least some need of an update.
*To make any solid claims concerning Armenians in Urartu is to my mind at least somewhat speculative and more a product of modern nationalism than anything else. But it has certainly shaped the kinds of projects undertaken in Armenia today.