Don't focus on the unit choices because they look very average (with the notable exception of Warplock Jezzails & unbreakable Rat Swarms). Look to the army special rules and unit special rules. Therein lies the answer to why these critters win so many tournament battles.
Here are the key advantages of a Skaven army.
Rank Bonus to Leadership
this is the foremost benefit of fielding Skaven on the battlefield. You get to add up to 3 to your leadership from ranking your units. Given the cheap points cost of units this is a massive bonus. You have to do this anyway really because leadership is generally poor but it's effecr is to raise leadership to above average or good.
Lead from the back
These pesky rodents are not too brave and can opt to 'lead' from the back. This means that you get to benefit from your character's Ld throughout a whole combat until conclusion - he/she or it, will be the last to perish.
Again, this is a tactic you should employ when fighting enemy rank and file troops. You're likely to rout but it doesn't matter as much (see below)
Run Away - to fight another day
This special army rule means you are move likely to escape alive when you rout (about 15% greater chance of survival that other routing foot troops)
Fire into Combat
Not a huge bonus but a great way of tying quality enemy troops up with cheap deeply ranked units and then using breath template weapons against them
great unit combinations I have spotted so far ...
rat swarms - unbreakable with Warplock Jezzails behind them (36" str 6 BS 3) and no line of site blocking.
Also of note:
lots of tactical options, high movement for charge, maneuver and no need for expensive cavalry. Also, a potentially devastating magical weapon (more to come on this).
That's it for now, I am still analysing the lists, I'll be back with more soon.