My noob attempt at an eagle deck to go with "Girl Power" for the "Return to Mirkwood" quest. Worked on the first try, incredibly. The synergy with Eagles of the Misty Mountains is crazy.
Strategy:
A good opening hand seems to be Winged Guardian and Eagles of the Misty Mountains. Winged guardian frees up Thalin and Theodred for questing, and Eagles of the Misty Mountains just grows bigger and bigger as the cheaper eagles die or leave play, and can soon one-shot everything. Pump up legolas' attack, and use him to snipe enemies and power through the quests. Sneak attack + gandalf is key as well. If you don't have it, try to use Beravor in the other deck to get it.
Re: Horn of Gondor. This was recently errata'd to only take effect when characters are destroyed. I prefer to play with the old rules for Mirkwood, because it seems clearly designed to work with Eagles. It is only later sets (I don't own) that completely break it. (It is quite possible to beat the quest with this deck and the new rule though.)
Heroes: Legolas is the least optional. You need to be able to kill things quickly (especially monsters engaging the spirit/lore deck) and make progress on quests. Thalin is key for Eastern Crows, and his ability is just generally really good for this quest. 1 damage on a Hill Troll can matter a LOT. Theodred is here because this deck will have problems generating enough tactics resources until you draw Song of Battle, and he is less threat than Gloin (who is not needed to block due to eagles) and helps the 2nd player deck as well.