Roman

Roman spatha’s where in part a response to the swords of the Germanic tribes, having similar blade types.

Roman axes are mainly infantry kit tools for entrenchment and fortification. Although I highly suspect they would have been used in battle if absolutely necessary, such as in the case of ambush.

Germanic

La Tene sword hilts where mostly wood with metal bolsters, as such most handle reconstructions are speculative

Migration Era axes are lacking in proper typology but are generally best represented by Petersen types A, B, C & Kirpichnikov types I, II, III.

The Viking age was a heyday for axe typologies; the increased proclivity of mail Armour increased the demand for heavier mass transfer weaponry than could still deal equally with lighter equipped opponents. The relatively cheap cost compared to swords of the period also contributed to their popularity among the opportunistic…

Spears are the most common dedicated military weapon of the Viking age, axes among the lower casts often met dual purposes and swords where status symbols of the most fortunate. However the spears purpose was for fighting and few men would ignore sage advice to brave the roads without their iron tipped walking staves.

Swords of the Viking age are easily the most diverse typological group of weapons. Regional stylizations where rampant and the constant seafaring movement of trade and raids saw a good dispersal of styles across western Europe.

Seax are a mix of tool knives and war knives that saw widespread use in the early Viking age as less expensive higher status backup weaponry; steadily falling off in favor of dual edged swords. The concept would forever live on into the medieval period proper in the form of falchions and messers.

Polearms are extremely diverse category of medieval arms making typologies difficult. If you can think of something that looked cool on the end of a stick its probably been done in some capacity.

Two handed axes almost universally developed into what we would call poleaxes / pollaxes having various combinations of spikes, hammers and blades in one weapon, often carried as primary weapons by the heaviest armored combatants such as knights.

Medieval Maces and Warhammers where a response to cut resistant armors such as gambeson and chainmail that saw prolific use in the 12th & 13th centuries. By the 14th century armour technology had mostly out paced short blunt mass weaponry however they continued to see use as non-lethal (well kind of) options for law enforcement and ransom hunting.

Battle Axes continued to be used as general purpose mass transfer weapons.

Sword preservation has been a bit better in japan due to the nation holding such high regard for swords. meaning we have pretty good examples over the last 10 centuries, problem being the changes are so minor it makes a general typology difficult outside size variation.

Left & right, The Japanese Sword Museum 2021 sword types by period

These are nomenclature diagrams for the different variations within the tachi and katana typologies. images like these are a dime a dozen and are not typically associated with archeology academic sources.