I get asked this a lot, and there's some confusion as to what the different slay multipliers are, and I had some of them wrong, too. So, here's the dirt... straight from the sourcecode in src/server/cmd1.c:
Slay Mulipliers
Whichever is the highest versus the monster you're fighting will be used. So, if you have a weapon with Slay Evil, Slay Undead, and Xdragon, the damage will be x5 versus a dracolich, x3 versus a lich, and x2 versus a beholder.
Slay Animal: x2
Slay Evil: x2
Slay Undead: x3
Slay Demon: x3
Slay Orc: x3
Slay Troll: x3
Slay Giant: x3
Slay Dragon: x3
Execute Dragon: x5
Also, there are hooks in the server code for items with execute animal/evil/undead/demon/orc/troll/giant, but from what I can see these seem to be leftovers from old items in earlier versions which were removed. The code is pretty spaghetti, so it's a litle hard to tell by just looking.
*Slay* Items
*Slay* items have the same multipler as Slay items, but three add a special ability to the item:
*Slay* Animal: Regeneration
*Slay* Evil: Blessed (random extra ego ability), wieldable by priests/paladins without penalty
*Slay* Undead: See Invisible
In case you don't know, the ego abilities are Feather Falling, Light, See Invisible, Telepathy, Slow Digestion, Regeneration, Free Action, and Hold Life.
Beyond this, the *Slay* items have a trailing bonus in parenthesis, which is a stat bonus. The stats affected by *Slay* weapons are:
*Slay* Animal: INT
*Slay* Evil: WIS
*Slay* Undead: WIS
*Slay* Demon: INT
*Slay* Orc: DEX
*Slay* Troll: STR
*Slay* Giant: STR
*Slay* Dragon: CON
Extra Damage Dice
Sometimes, excellent weapons and ammo can have one extra damage die. This means seeker arrows can be 5d4, broad swords can be 3d5, etcetera. It's pretty rare, though... and it's based upon the original item dice, so the more dice an item has, and the more damage each die is, the less likely it is to have added dice. The chance of this happening is 1 in (dice * damage *10)... so for arrows, it's 1 in 40 ( 1 * 4 * 10), for seekers, it's 1 in 160 (4 * 4 * 10), and for a Mace of Disruption, it's 1 in 300. This is an additional roll made once the item has been determined to be an excellent, so... don't hold your breath.
Excellents
As for how the game determines when an item should be an excellent, this has to do with all sorts of voodoo based upon the 'power' of a level, the depth you are at, and a few other things which I haven't bothered to decipher completely yet... but suffice it to say, that there's a range which widens the deeper you go. The deeper you are, the more likely you are to have a level that's far better (or worse) than you are at shallower depths, and the items you find there are based upon that level 'power'.
Hope this helps...