Nehan:
A game against dwarfs is a very specific game - “who has better eye and better rolls” - simply put, hide earthshakers from cannons and ubergrudgethrowers. Use bolt throwers to (hopefully) destroy organ guns in the first place. Remember about rune of challenge, keep taurus out of its range, yet use him as the only means of killing anvil runelord (as opponent will likely deploy him somewhere when he cannot be targeted from bolts).
Border Reiver:
Facing a unit with an oathstone is dead simple - force him to drop the oathstone with a charge to the flank of the unit (wolfriders are best for this, but BC are quite useful as well, since they will be percieved as a major threat). Hope that you flanking unit breaks and runs (hopefully to rally again - you are putting a musician in with your units I trust). Now the Oathstone unit is immobile.
It is now a target for your bolthrowers, and other artillery, and right now, it is perfectly safe to march your blunderbuss unit right up into his face and unload - repeat as necessary.
BLOOD AXE:
Greetings my evil kin.
ANVIL OF DOOM
One of the biggest perceived threats in the Dwarf list is the Anvil of Doom. Yes,it can have alarge effect on the game(if he is lucky), but it is also a large chunk of points in 2K. It will be about 400 points, maybe more if he loads up on Runes.
-The Anvil’s powers are used in shooting phase, so it seems it should be effected by the Earthshaker. So if you fire your Earthshaker cannons near his Anvil, you have a good chance of stopping it next turn.(4+ warmachine)
-The Anvil’s powers can’t be used if its locked in combat. Possibly some fast Wolfriders can hold it up for awhile. olfriders will be seen as a lesser threat then Bull Centaurs. I doubt any Dwarf Genersal would let you get a unit of Bull Centaurs inm his deployment zone. If you manage this,it seems the battle is going well already!
-Flyers like the Taurus & Lammassu should make short work of the RuneLord & Anvil. Challenge him!!! The RuneLord must accept, the Anvil Guards will stand back & do nothing. They can be slaughtered next turn. Beware though, a smart RuneLord will target your flying monstrosities first, robbing them of their wings! They are still pretty fast with M6.
-An inexperienced Dwarf General can be his own worst enemy & your best ally. Let him keep banging away on the Anvil trying for Ancient Power. Eventually he’ll fluff his roll and the Anvil could explode netting you the VP’s!
HAIL HASHUT!
BLOOD AXE:
:cheers Great model, but its 1,000 points, so not a popular option in a 2K game. 
Ancient History:
I distilled this thread into a Chaos Dwarfs vs Dwarfs page on the Wiki, linked off the Chaos Dwarf Tactics page.
Cryonicleech:
I generally try to shoot at the warmachines, due to what I see as an “Over Reliance” on ranged firepower, but that’s no guarantee.
Haven’t dealt with the Anvil yet (My main opponents are Empire,Bretonnia/ Lizardmen) but all I can say is shoot it. It may have a +4 ward, but he’s gonna miss SOME of those, and hopefully you kill the Runelord…