Tips on killing elementals

[Ixal]

Cheesy way, neutral monsters don't react to being attacked from 3 hexes away. So get that catapult(s)

 

[Peter Ebbesen]

I use mostly medium or strong melee units to kill them. Just take endurance on level up, cast an elemental resistance spell (2 if you can) and buy enchanted weapons, silver weapons, or some other perk to help kill them faster. This method requires you to cast healing or a damaging spell, but overall it is pretty simple and doesn't require to many units.

True, but I am not sure it really addresses the OP's particular situation (human, early game expansion blocked by greater fire elementals, low research). I mean, it is nice if you have the resources and spells to pull it off, but odds are against it in the early game.

 

[unacomn]

The best way I found for Elemental genocide would be trough obtaining one pack of Wolves of Helia. I let one loose in a desert-like world that was filled with elementals and dragons. Everything there died. The pack of wolves was hardly scratched.
Note: Cast levitate on werewolves before turning them into Wolves of Helia, you would be able to after.

 

[camelotcrusade]

In today's game I found an unexpected way to kill a Greater fire elemental that was terrorizing an area of my map. I summoned a standard fire elemental and cast elemental resistance on it and frost weapon. Took a few rounds, but I dealt more damage than I took (and when the regen perk came up, I grabbed it) and managed to get rid of it that way. Plus, when you're done have a nice leveled up elemental to throw at something else, too.