Aktually the Valar have their own Maiar armies (Sauron, Gandalf, Balrogs are also Maiar).
Its just that most elves live in Valinor and go to war together with the Ainur (Maiar+Valar) as they have the same enemys and understanding of evil, but it only happende once since the elves live there.
But they are quite reluctant at waging wars as they are so powerfull that their intervention literally shapes the world new (their last war sunk the entire region the first Age took place in, into the ocean) and thus has consequences they can't foresee themselves.
Also as I understood the Valar gave up their dominion over Arda in exchange when Aman (the continent(?) where Valinor lies) was removed from the world and Numenor sunk, both done by Eru, or elvisch Ilúvatar (God), and will only return once more (at the apocalypse) to fight the fallen Valar Morgoth, Saurons master, when he returns to Arda (Earth).
Edit: Also I'm quite sure that Orcs and Goblins are ment to be the same in Tolkiens universe.
Edit2: Valar (perhaps with the exception of Morgoth) don't see themselves as Gods (they are perhaps more like Angels with demigod powers?). They are the Powers of Arda. Eru is the God, the only one who can truely create new life, and they have met him and tell about him. But as only at the beginning of the First Age someone (the Noldor) actually left Valinor to live in Middle Earth and so many of them died fighting Morgoth this knowledge isn't wide spread in ME and the "lesser" human people see them as Gods (simmilar to the Nordic or Greek Gods) as they can't know better.