Ok, I'll give it a quick go...I'm sure I won't have all the details 100%, so anyone, step in to correct mistakes!
For books, I'll categorize as "new" (within the past year or so), "older" (have a few years under their belts), and "outdated" (in need of being redone, though not necessarily with one planned)
Beasts of Chaos: no book right now, apparently one in the works for a soon-ish release. Largely a skirmishing army, allowing for more freedom of movement that the standard regimented ones. Low armour, average strength troops, supported by larger monsters (ogres, giants, trolls..)
Hordes of Chaos: new book; generally a quality over quantity type of army, focusing on close combat (next to no shooting), with good magic.
Demons of Chaos: new book; definitely a quality over quantity style, close combat/magic oriented. Widely thought to be way overpowered. You won't get too many eager opponents outside of tournaments.
Brettonia: old book; focus on elite cavalry units, with low strength/skill rank and file support.
Empire: old book; the most flexible of armies. You have access to units that allow you to focus on any of speed, magic, or shooting. I hesitate to put close combat in there as well, as I think the Empire lacks a strong enough presence of elite troops to overwhelm opponents in combat, but I suppose a case can be made for it with the right combination.. Sure, there are armies out there that will beat the empire in one or two of those categories, but I don't think any other one can compete in all 4.
Dark Elves: new book; fast infantry, with good shooting and high quality close combat troops. Down side is toughness. All elves tend to fall over in a stiff breeze. Magic level is average, I would say.
High Elves: new-ish book; similar points to Dark Elves in regards to infantry, shooting (Dark Elves have a bit more), close combat and low toughness, with the following differences: magic level is much higher, and there is a higher focus on elite troops, meaning the organization chart is different, allowing you to field more. Granted, this means less models on the table, as the elite troops cost more, but that's part of their charm.
Wood Elves: old book; standard elf movement (with the bonus of not being slowed down by forests) and toughness. Fantastic shooting..no war machines, but bows pretty much everywhere. Tree spirits (dryads, tree-kin and treemen) for close combat support.
Skaven: outdated book (I believe it is the oldest one in print right now); the prototypical horde army. It is not difficult to outnumber your opponent 2 (or even 3) to 1.. Low quality troops, but with strength in numbers. Magic can be high level, and is mainly direct damage minded, with some shooting thrown in for good measure. Down sides include the low skill and toughness of troops, a low leadership across the entire army, and the unreliability of guns/war machines. There's a good chance things will back-fire on you at some point in the game. Again, part of their charm.
Ogre Kingdoms: outdated book; considered one of the weaker armies. Low model count (so a dream for slow painters!
) , but above average strength and toughness. Good infantry speed, multi-wound rank and file, average leadership. Also, cannon fodder in the form of gnoblar (hill goblin) troops. On the down side, low magic, shooting, and weapon skill, next to no armour.
Tomb Kings: really outdated book; along with Ogres, one of the weaker armies. Reliable (though really low quality) troops, as they will never run away. Most reliable magic, with no chance of failure, unless opponent stops it. Lacks offensive punch compared with newer armies, and most of unique perks were also given to new Vampire Counts.
Vampire Counts: new book. No shooting at all, but reliable troops (as with Tomb Kings). Excellent magic to replenish fallen rank and file, which make for a very powerful army when your troops don't run away, and can be easily brought back should they fall. Along with the Demon army, the most powerful ones out at this point.
Dwarves: old book. Reliable, resilient troops. Fantastic war machines, and great shooting. Slow army, but tough enough to take the abuse before engaging in close combat. No magic at all, but good magic protection.
Orcs and Goblins: old book. Take what I said about Dwarves, and the opposite is just about right for Orcs and Goblins. Low leadership, poorly armoured, squabbling troops, questionable war machines and poor shooting. However, when they do hit, they do serious damage. That, and they have numbers on their side. ...as well as chariots, cavalry, and giants, to mention just a few. Just be prepared for mayhem (and good laughs!), as your forces have the potential at times to do as much damage to yourself as your enemy. Magic levels can be very good.
Lizardmen: new book (currently the newest, actually); I have yet to face off against the new lizardmen, so I'll leave that army for someone else.
All these have been from my own experiences, so others' opinions may vary. Hope that helps!