The Four Essences' of the Elements

ELEMENTAL INVASION: Every few days, this event you have described occurs. A boss is spawned along with a portal that spawns "Elemental Invaders". The one in Silithus pops out The Windreaver and its Whirling Invaders that drop Essences of Air, the one in Un'Goro pops out Baron Charr and his Blazing Invaders that drop Essences of Fire, the one in Winterspring pops out Princess Tempestria and her Watery Invaders that drop Essences of Water, and the one in Azshara pops out Avalanchion and his Thundering Invaders that drop Essences of Earth. The drop rates are like this: The Elemental Invaders have a higher drop rate than normal mobs for essences, and the Boss has a guaranteed Essence drop. Here's the catch: If you kill the boss, as you said, the Invaders go away. So the whole area will be mad at you if you kill the respective boss, especially the one in Silithus, because the Essence of Air drops are abysmal from the Dust Stormers. Balance the benefits and risks to killing the boss, and have fun! 

Fire: http://www.thottbot.com/?i=10062
transmutes - Air to Fire
You can farm essence of fire from elementals in middle ungoro crater (or AH them for 4-5g)
found 4 of these in about 10 minutes of killing at Fire Plume Ridge in Un'Goro.
I got 2 of these in 80mins of killing in Felwood (entropic horrors)
spent 10min and killed about 10 fire elementals and got 2 in burning steppes



Air: http://www.thottbot.com/?i=18574
transmutes - Water to Air
killed about dust stormers out at silithus after the 1.7 patch and got 1 essence of air. 
Ok here are the stats I compiled over 2 days of farming for Essence of Air in Silithus.
Day one: 1 hour and 15 minutes of farming.
I killed 68 mobs. (all Dust Stormers)
Dropped goods:
-2 Breath of Winds
-8 Elemental Airs
-1 Purple item (Eye of Flame)
Day two: 6 hours and 32 minutes of farming.
I killed 307 mobs. (all Dust Stormers)
Dropped Goods:
-15 Breath of Winds
-22 Elemental Airs
-2 Essence of Airs
-3 random Green item's 
The proposed patch notes on the WoW site states the drop rate for Essence of Airs will be buffed.
after patch 487 Dust Stormer's Killed:
- 8x  Essence of Air
- 27x Elemental Air
- 20x Breath of Wind
- 10x Random Green Items 



Earth: http://www.thottbot.com/?i=7534
transmute: Fire to Earth
transmute: Life to Earth
got a Essence of Earth and Core of Earth from n silithus off  Desert Rumbler (21, 15)
found in silithus off  Desert Rumbler (21, 15) got 2 drops in about 25 mins
got 4 in less than an hour in crystal vale killing those rocks, i am a mage and i aoe 3 at a time
Got 3 in a day just roaming around Burning Steppes killing greater obsidian elementals




Water: http://www.thottbot.com/?i=8126
Transmute Earth to Water
Transmute Undeath to Water
You can farm essence of water from toxic horrors in Felwood (or AH them for 10-12g)
Well, I grinded for an hour in Felwood, and got 9 essences, maybe I just got lucky..
They can drop off the elemental water types, globes, elemental, and essence.  Nothing else