So I played my first game against Skaven and lost, mostly because I underestimated the hitting power of the Abomination. This thing is more broken than the War Hydra or Vargulf. It killed like 12 dwarfs on the charge (rolled a 6 on his S6 impact hits!). However, on the first 2 turns it moved forward at a very slow rate due to some bad rolling for its 3 D6 movement, so I was able to wound it with my flaming cannon.
Note that wounding it with a flaming weapon prevents it from coming back to life. All of the different attacks it used against me ignore armor saves, one of which does a Strength 6 hit and D3 wounds to everything in base contact, so don't count on Dwarf characters being capable of finishing it off after surviving your shooting. All shooting has to be put into this thing.
Note that it can't be march-blocked.

The SCreaming Bell is very good, and it will be a common centerpiece for Skaven armies. Its unbreakable and the Grey Seer have a 4+ Ward Save so it can't be shot reliably, and if its shot with something higher than S5 the bell is activated, so another minus. On the other hand, its abilities often kill a bunch of the rats pushing it, which, combined with your own focus fire, can maybe cause the unit to reach less than or equal to Unit Strength 10 and thus slow its move. THis is useful because the Grey seer CAN be targeted by models in base contact with the bell, and thus easily be slain by a good lord or thane in 1-2 rounds of combat.
Note that if a Grey Seer is on the Bell he can't Skitterleap away! So if you force him into combat, he's stuck there.

The plague furnace was not in the game. But it has no save and thus can be targeted and killed relatively easily. It is however, ridiculously good on paper so its yet another thing in their army that likely HAS to be shot...

Their magic is pretty good, but not OP--I managed to protect myself pretty well with only 5 dice and 2 runes of breaking, and they are just as vulnerable to taking damage from it themselves as before. Look out for Wither, which decreases a unit's Toughness by 1 for the REST OF THE GAME, and casts on an 8. Also look out for Scorch, at S4 it might not seem that bad, but like everything else in their army its template is no partials and can be places on anywhere the Skaven player wishes within 24'', no line of sight required. They have no way of selecting spells, so you won't be facing wither AND Scorch every game. But if it happens, stop it at Wither and take the Scorch damage if necessary.

As for shooting...big time nerfing done here. I was not impressed by their shooting. Ratling guns are pretty bad as they misfire the same way as before but also require rolls to hit now, and don't get much through. Their new stone-thrower style war machine is alright, but not against dwarfs at only S2. The things we have to worry about are the mortar weapon team and Warp fire thrower. The latter is vastly improved this edition with longer range, I think, and no partial Flame Template. The mortar is also no partial, as are all template attacks in the book, and wounds on a 5+ no armor saves allowed, 24'' range.

I take heart in the fact that Dwarfs are one of the best equipped armies for dealing with the Abomination and Plague FUrnace with ranged attacks. Also, dwarfs are very capable of weathering their ranged assault to try and get close to their Grey Seer if they make a mistake. The trick is to slow down the Bell, or threaten his non-unbreakable units with characters in them enough that he decides to protect them with the unbreakable Bell block.

Good Luck Everybody!