If you don't have Lava Shock to cancel out all that overload, then you just wind up in a position where you need to use aoe two turns later since you effectively forfeit your next turn and probably just wiped your own board. I really don't understand why they made it hit your own minions. It has negative totem synergy.
Let's talk about this. Since I actually find it has way more utility beyond just AoE.
First off, it should be said
never use Elemental Destruction at 3 mana. It is not a 3 mana card unless under the most extreme circumstances.
Now we've established that rule, there are a number of ways you might get more out of the card. There are some benefits on turn 4, but I think for the most part Elemental Destruction is a
turn 5 and up card, minimum. Let's take a look.
Overload - The easiest to grasp. If you're going to be Overloaded never turn, unable to play much, why not go the full distance? AoE, then drop a Totem Golem. Or use Ancestral Knowledge for card draw. At some point, extra overload stops mattering.
Card Draw - Speaking of Card draw, you can play a Loot Horder or a Bloodmage Thalnos to cycle when you AoE, which isn't possible with Lightning Storm (Bloodmage will also boost that AoE up to 5-6 points of damage). Or, play an Acolyte of Pain or 2 a turn earlier. Since Elemental Destruction is
damage and not
destruction, it'll trigger.
Spell Power - Speaking of damage, you can increase the power of the AoE with things like Bloodmage or Kobold Geomancer. However, for the most bang for your buck, put down an Explosive Sheep for
6-7 points of damage, giving you the strongest-cheapest AoE in the game.
Deathrattle/Damage - In general, Deathrattle is good with Elemental Destruction. Pop a Nerubian Egg down, clear their board while simultaneously filling yours. No more relying on a single activator. Same with Dragon Egg(s), which trigger off your AoE. Try a Leper Gnome if you want face damage. Or a Haunted Creeper. Give an existing Minion on the board 'Ancestral Spirit' so it'll pop back up alive. Got a Shredder? Play it a turn before hand. Tie it all off with a Baron Rivendare--with 7 HP it'll survive the AoE and double your deathrattles.
Also, because you're killing your own minions, if there is a 6 minion minimum on the board between you and your opponent, you'll be able to play Volcanic Drake
for free.
Mechs - Cheapo mechs work well towards repopulating your board. Mech Warper, Annoy-o-tron, Clockwork Gnome.
Minions in general - Cheap minions like Worgen Infiltrator, Zombie Chow, Echoing Ooze do the same.
Lava Shock - Lava Shock will clear your crystals for the following turn, so you can play it out like normal. And say your AoE doesn't get everybody, Lava Shock will finish the job.
Doomsayer - Here's something I would love to try. Use Elemental Destruction for a clear, then drop Doomsayer. Since you might be unable to do anything next turn cause of Overload, Doomsayer might by you some time. It discourages them from playing anything worthwhile. If they want to kill it, they'll expend some resources to do it, like perhaps a big spell or a Silence.
Totem: And, if nothing else, you can play a totem after a turn 5 Elemental Destruction.
Of course, all the cheap Shaman cost cards can be combo'd with it obviously, like Earth Shock, Lightning Bolt, Rockbiter Weapon. It goes without saying that later turns will enable crazier tactics, but the ones I listed seem good at any mana level.