Can't make out how to play with Dwarves... :(

[Relf]

Dwarven Calvary is ranged/artillery.

I like to have at least one thrower in my army composition, it forces orks AI to charge you. It's also responsible for one of the cavalry jobs, use your artillery to hammer down on foes that lose morale and start running both to keep them from regrouping and to make sure they take maximum damage before leaving the field.

As everyone else says, you need a strong battle line, first of Dwarf Warriors, then adding some longbeards, then some ironbreakers. 2/3rds of your melee troops will be in that initial line, the remaining 1/3rd will form a reserve for handling flankers be they cavalry, fliers or just troops that spill over because I make my line deep and short rather than thin and long when playing Dwarves. This is both because you really don't want them getting engaged by 3 enemy troop groups at once and because them Dawi don't move so fast, keeping distances short is to your benefit.

The other cavalry job of being the hammer to your melee anvil is handled by your ranged units. My order of love is Quarrelers, Thunderers, Rangers, Miners with Blasting Charges and finally Irondrakes. Start them off near the edges of your troop lines, after your reserve runs interference on the enemy flankers you run them out behind the enemy line fighting with your Dawi Battle Line and let them unload on the enemy from behind. I'll frequently finish battles against the Greenskins with ~50 kills per unit on the melee and 100-300 on the ranged guys as they just pour death on their enemies from behind. Dwarf Lords and Heroes to square off with enemy heroes and lords, if you have any extra, you can toss them in the Battle Line if they're slow or in the Reserves if they're a bit faster.

[CDRChance]

Wow, it's interesting to see how completely different an experience people can have playing the same game. I've always considered the dwarves the easiest race to play, and one of my favorite. I only played H/H on TWW1. The only real rough campaign I had with them was the DLC faction who had the 50% upkeep penalty and had to fight against the DLC uber-goblins. The OP's description of his battles with dwarf warriors and quarrelers against orks doesn't sound anything like what I was used to. Maybe guard function to keep your quarellers from chasing targets when they run out of range?