Heroes 5.5 WarGame Edition - Tactical Edition.

Bandits, beastmasters, defilers (or goblin bandits, goblin beastmasters, goblin defilers)

I think it would be better to rename Bandits to Raiders. Simply "bandit" is associated with more modern, organized crime, and not with a primitive people who rob caravans. Otherwise, it's fine; "goblin" is an unnecessary clarification.

Vultures, asps, wyverns

I don't understand what this lineup is... Are there really any birds and snakes there, or are they all wyverns? You could use other creatures in the name. Salamanders, for example. Or have they already been assigned to the dwarven dragons? I don't remember.
An echidna is also a mythical creature.
Should vultures be renamed to scavengers?

Stormtroopers, executioners, leaders (or thugs, executioners, leaders)

The second option is better; the first one sounds like something from sci-fi.

Gladiators, punishers, giants (or minotaur gladiators, minotaur punishers, minotaur giants)

The first option is fine.
In general, you can play on the fact that "minotaur" doesn't have to be the name of the entire race. Just like a giant, it's originally a proper name.
That is, make it gladiators, punishers, minotaurs.

Thanes, jarls, thurses

I've said it before, I like Aesir the most, not thurses. In fact, Thor is a specific case of an Aesir.
Scandinavian mythology is popular now, and it's unlikely that many people will misinterpret this name.
You could also call them Jotunn... But then you need a corresponding icy theme for this tier. Jotunn is an ice giant, not just any giant.

Engineers, arsonists, saboteurs (or gremlins-engineers, gremlins-arsonists, gremlins-saboteurs)

The first option is fine.