Kataibates

Zeus, the god of lightning, had a nickname "Kataibates" (he who descends). This basically equated Zeus with Thunder/Lightning...

Pic: Antikenabteilung, Staatliche Museen zu Berlin—Preussischer Kulturbesitz

Remember this article about what came first: Thunder/Lightning or Thunder God? Thunder gods of course...

The piece of ground hit by lightning cannot be walked on, is consecrated to Zeus and is marked by a monument or an altar. These altars were then used to make offerings to Zeus in exchange for protection from lightning...

Same altars dedicated to Zeus Kataibates were also built in front of houses, and there too offerings were made in order to protect the house from lightning. This custom seems to have been fairly common in Greece. 

You can read more about this in "Greek Popular Religion" by Martin P. Nilsson...

Interestingly, Zeus's thunderbolt was imagined to be a stone or a stone axe. Like this one. 

Which is interesting considering that Zeus didn't wield an axe...Well that't not exactly true. Late Roman god Jupiter Dolichenus, whose mystery cult was widespread in the Roman Empire from the early-2nd to mid-3rd centuries AD, wielded an axe. And rode on a bull... Here is an altar from Vindolanda dedicated to Jupiter Dolichenus...

Pic: www.digitalmedievalist.com

It is believed that he came from the east...And in the east, in Anatolia, we find Hittite thunder god(s) wielding an axe...

Pic: www.mesopotamiangods.com

And even further east we find Adad, Mesopotamian storm god, who also loved axes...

Pic: History of Egypt, Chaldea, Syria, Babylonia and Assyria, Vol. III

How far East and how far back in time should we go?

Stone axes or adzes, originally shaped and polished in Neolithic times, sometimes turn up in later archaeological sites or graves from the Bronze Age down to the medieval period...

Because they were apparently thought to have some kind of magical power to protect buildings and people, especially from lightning and violent storms...

We know something about these beliefs thanks to a string of testimonia in technical treatises on stones, beginning with a third-century BCE Greek author named Sotacus and ending with a twelfth-century bishop of Rennes. And thanks to European folklore...

It is important to understand that there is no evidence that the Greeks or Romans realized that these axe-heads were manufactured by previous stone-age cultures. They were believed to be “natural” stones which, like amber, jet or coral, had special protective powers...

Sotacus, the Hellenistic author of a lost treatise on stones maintained (according to Pliny’s abridged account) that "cerauniae are similar to axes" except they are not axes but magic thunderstones...

Latin lapidary (natural history) attributed to Damigeron-Evax, devotes an entire chapter (12) to the "lapis ceraunius" (thunderstone), which is found in places where lightning has struck...

Timotheos of Gaza, a 5th c. CE author tells us that "you will have an amulet against a thunderblast (keraunon), if you inscribe a thunderstone (lithon keraunion) with the letters αφια αφρυξ and keep it in your house"

In his Etymologies Isidore, the early 7th c. CE bishop of Seville, also notes that "ceraunia" (thunderstones), were found in places struck by lightening and could avert lightening...

In the 12th c. AD, Marbodaeus, the bishop of Rennes, preserves a similar account in his own Liber lapidum.

And in the 11th century the Byzantine emperor sent to the Holy Roman emperor a "heaven axe" as a present...

Ethnographers and folklorists have also established the existence of similar long-standing and widespread beliefs throughout Europe.

For instance, in modern Greece, astropelékia ("lightening axes") are sought out at places where "lightning has fallen" and are kept in houses to ward off lightning and fire...

Perun, Slavic thunder god, also wielded an axe...According to Slavic folk beliefs, prehistoric stone axes found in the ground were remains of these weapons...

Thor wielded a hammer...And we know that in Scandinavia thunderstones were frequently worshiped as family totems which kept off spells and witchcraft...

Both Slavs and Scandinavians wore axe (hammer) amulets...

Thor's hammer amulet

Pic: Sveriges hednatid, samt medeltid, förra skedet, från år 1060 till år 1350

Perun's axe amulet

Pic: Древнерусские амулеты-топорики

I always thought that Thor's hammer looked like a stylized axe

That Thor's "hammer" was originally an axe, can be seen from this next artifact. A museum in Utrecht has a relic called "the hammer of St. Martin of Tours". 

Pic: Museum Catharijneconvent

The "hammer" was made in the 13th or 14th c. from a Bronze Age stone axe dated to 1,000 - 700 BC...

What does this have to do with Thunder gods? Well, St Martin is another "saint" who is nothing more than the thunder god in disguise. I talked about this in my post The "The axe of Martin"...

Another indication that Thor's hammer was originally an axe, can be seen from the etymology of the the Thor's axe name: Mjǫllnir. The etymology of the hammer's name is disputed among historical linguists.

Here are proposed etymologies. You tell me which one is most plausible:

1. Old Norse Mjǫllnir developed from Proto-Norse *melluniaR and one proposed derivation connects this form to Old Church Slavonic mlunuji and Russian molnija meaning 'lightning' (either borrowed from a Slavic source or both stemming from a common source) and subsequently yielding the meaning 'lightning-maker'. 

2. Another proposal connects Mjǫllnir to Old Norse mjǫll meaning 'new snow' and modern Icelandic mjalli meaning 'the color white', rendering Mjǫllnir as 'shining lightning weapon'. 

3. Finally, another proposal connects Old Norse Mjǫllnir to Old Norse mala meaning 'to grind' and Gothic malwjan 'to grind', yielding Mjǫllnir as meaning 'the grinder'.

Considering the amount of mixing between Slavs and Norse and mutual cultural influences...

Also, The word "mo(ld)nya" (lightning) exists in all Slavic languages. It's cognates, apart from Norse Mjǫllnir are: Latvian "milna" (hammer of the thunderer 🙂), Old Prussian "mealde" (lightning), Middle Welsh "mellt, myllt" (lightning)...So...

Archaeological evidence confirms, that this belief in the link between Thunder Gods and stone axes, and the belief in their protective power was already widespread all over early Roman Empire.

For instance, in a survey of pre-historic axe-heads found in Roman sites in Britain, of the forty known examples, twenty nine were found in or closely associated with buildings...Some in temples...

You can read more about this in "Inscribed Greek Thunderstones as House- and Body-Amulets in Roman Imperial Times". 

The generally accepted belief was that a thunderstone fallen from the sky will in future protect against thunderstorms and lightning strikes. It's power will be greatly increased if inscribed with a magic spell...Like this roman example with Greek inscription...

Pic: www.nat.museum-digital.de

Or like this Roman stone axe amulet worn as a protection against evil...Lightning too...

Pic: Inscribed Greek Thunderstones as House- and Body-Amulets in Roman Imperial Times

So...

Are European folk beliefs related to the thunderstones Roman in origin?

Are Roman beliefs related to thunderstones Greek in origin?

Are Greek beliefs related to thunderstones Hittite in origin?

Are Hittite beliefs in thunder gods armed with an axe Mesopotamian in origin?

Where and when does the link between the stone axe and thunder god originate?

I would suggest that this link between a stone, more specifically flint axe, and thunder gods, already existed in the 4th millennium BC Europe...Enter exploding flint axes dudes from Southern Baltic... 

Pic: www.naturstyrelsen.dk