Well, completely smoked my "killer stack" that nothing - and I mean NOTHING - else could stand up to. Any strategies for beating dragons?

Yes, the "Dragon Form" scroll.
Transforms a friendly unit into a dragon.
Oh and an added bonus: That friendly unit gains (and keeps) the experience for slaying a dragon as well.

Other than that:
A highly resistant fighter or archer and a couple of unicorns at level 20 could do the trick as well.

dragons on their own aren't that hard - a level 20 scout with a good bow and some units that can be spared is able to kill it in 2 or 3 rounds - just double shot him all the time - archery will overcome his ranged defense and so at least i deal something like 20 damage per shot (high morale is awesome) two shots per round - and thats a dead dragon
same goes for a level 20 warrior
a wizard without the dragonform has a harder time - those dragons are completely magic immune - so he has to rely on his troops - well i guess a good unit with fire blade should be able to do the trick as well
a commander on the other hand has a rather hard time against those but i will try it tomorrow (my commander got the "kill the dragon" quest and i want that reward)

the cult of the dragon are a completely other story- they have a dragon (on a higher level than the lone ones) and he is backed up by some griffins monk and the tier 3 healers - nasty stuff
but again doable with a highlevel scout or warrior (well a level 27 sharpshooter/chieftain with a team full of centaurs roflstomps everything i have met so far)

Spiders (or spider and magic weapon spell) and any unit with high attack or lower attack with poison.
Dragons have an immunity to spells but it don't make an effect to spiders web =)

Oh, that's naughty.

Dragon poisoning?

That's not very sportsmen's like, is it?

:-)

You play football or Eador, don't you? ;)