You can't acquire them until the Orcs chapter when you can upgrade Armories into Breeding Grounds. As far as Orc production goes,
@RosehawkATA is right. Two is enough. If you have three, you've got all the Orcs you'll ever need. I have three Level 23 Armories, and 9 days out of five they're dormant. Without ever running them, I always stay above 40K Orcs, since the Heroes Forge (Level 2) gives 375 a day for free. That's enough to take care of all my needs.
That'll change soon, though. You need Orcs for two things: Catering Provinces and Upgrading Workshops. That's the only time I ever run my Armories: When Workshops need Orcs. Upgrading all four of my non-Magical Workshops to Level 25 should take under 20K orcs, so it's not like I'm in any danger anytime soon. But the point being: For Orcs, three is all you need but two is acceptable.
BUT: The reason I'm writing this whole post instead of just liking Rosehawk's comment (took me long enough to get around to it) There is a caveat. While two is alright for Orcs, four or even more is preferable if you're a fighter. I had four in Orcs chapter, and made the mistake of selling one and later my Dwarven Bulwark. The Level 3 Shrine of Shrooms and 3 Level 23 Armories are not nearly enough for my military needs. I'm trying to find a way to upgrade the military aspect of my city and already have a plan for the Bulwark as soon as I complete the rune wheel.
So while two is alright, it's not preferable for a heavy Expander. If you focus on negotiations (which I HATE doing, it's a huge Goods suck) two doesn't produce a whole lot of Orcs. If you're a heavy fighter, two doesn't give you enough training power. So two is alright if you are a mix of the two and don't go crazy on the Expansions.