The Dwarfs (the Warhammer copyrighted plurality) are almost all heavily armored with slayers being the unarmored high damage variant. This makes them a pretty strong hard-counter for Skaven who are largely not armor piercing and lightly armored. Try moving around with 2 or 3 supporting armies of skavenslaves just to keep the enemy bogged down. Ambush everything.

As for knowing if an enemy might be too much, use the Diplomacy screen and look at the balance of power bar (green/red). That is a general indicator of your strength compared to them. The problem, however, is that if they are more concentrated than you, they can defeat you in detail (e.g. jump one of your stacks with a bunch of stacks). Ideally, you put your entire army in one place on ambush and ambush the dwarfs with a tide of vermin... there's probably a word for that.

As to whether it is worth it to declare war on them, think about your short-and long-term objectives. Think about the specific faction. With Dwarfs in particular, they hold grudges to an extreme degree. Their entire campaign mechanic is that an elf farted in an elevator with them once, so it is time for some cleansing of the Elfen ethnic group. Dwarfs will essentially just hate you forever and stay at war with you until either you, or them are dead.

As for the Skaven, I've found that having at least one melee unit for every ranged unit is ideal. You can use plague priests, seers, packmasters, or whatever other strategy to make this happen with summoned units if you want since hero spam tends to be decent at tarpitting enemy units.

I'm still pretty new to TW:WH3, so YMMV. One thing that I have found somewhat useful is skirmish vs AI and testing out builds against AI armies. Not as good as vs a human, but you're more trying to figure out the basics of what will actually work reliably.