Well, if you are able to describe his army in more detail we could help more
However, general advice: Organguns or Flame Cannons are to be avoided. Organguns are still autohit artillery dice (as far as I am aware) and will tear you to pieces. The Flame Cannon is pretty nasty too. Try to get some boar boys or something like that to take them out though beware of lone Dragon slayers, these are some of the best artillery defence you can get.
Another sneaky tactic I have employed as a dwarf player is to stick a bolt thrower out on its own down the flank, with a rune of penetrating and the master rune of immolation. Because it is out on its own it seems like a tempting target so you send someone in to deal with it. Then BOOM! 2D6 str 5 auto hits.
Thunderers are deadly up close (that +1 to hit is nasty) and Quarrelers are good over long range. If you are marching down a gun line make sure you have a lot of models. A massive (40+) unit of gobbos likes to soak up wounds. I forget the name but the ball and chain guys are pretty deadly as well. especialy against CC units as they can't hit them back.
Orc & Gobbo artillery is like everything else in their army. You need lots of it to do anything good.
Magic is always a good mainstay of the Orcs however with the dwarf +2 to dispell everything, as well as a good number of dispel dice it is not always worth it unless you have a good few casters and tbh you want some good CC orcs to deal with the hard as nails Dwarfs.
Dwarfs mainstay in CC is not getting killed. They have a high toughness and good armour rating so killing them is difficult. They are not that strong though (Longbeards and characters are str 4 and hammerers and miners have great weapons) so they can't always strike back too hard. Just be careful of their elites though. Hammerers will destroy you if they get a chance to hit back, and Ironbreakers will just downright refuse to die.
Hope some of this is helpful.
Mind you, I am not sure how relevant all this is as I have not played a game with the new ruleset, so I would wait for someone to confirm my advice first.