Tactix skaven vs ONG

An assassin might work to deal with the BSB but have you considered just trying to kill the unit from range instead?

Try look at bringing some artillery to deal with the unit outside of their range. Something like a plague claw or some poison wind mortars to just mess with the unit from range. Given how squishy goblins are one or two decent hits will decimate the unit and drastically reduce how much damage they can put out

A nice vortex spell maybe?

Pillar of Fire from the battle magic lore is a good one to encourage blocks to move as it doesn't more randomly, you move it the direction you like (and it moves at start of both players turns).

It's d3+3 St 3 hits, so good against low T units like Goblins. At least 4 hits each time so on average 2 kills (6 kills if you roll well).

Get it to keep hitting the back of the unit so he's forced to either suffer it or advance.

I do like this but that sounds like a lore of fire spell to me. Warp lightening is obviously the most accessible spell but its OP for low T units i believe. Maybe scorch? I cant really think of any nice vortex spells for skaven at the minute but will give it a good look in thank you!

First, a few things to point out. 

1. The horde rule doesn’t increase the amount of models that can fire, still just the front two ranks, plus whatever volley fire (from the short bows) adds. 
2. Short bows are only 18” range. Anything past 9” will be -1 to hit. If he moves that’s an extra -1,  and volley fire won’t work. He can’t even get any shots off on a normal Battleline scenario if he went first. And range is measured on a per model basis, so his front rank may be in range, but his back ones could be out of range. Since you can always premeasure, and given the speed of skaven, you can just always stay 10” away and will still most likely make any charges against him, while he will either continue to have a -1 for range, or a -1 if he moves closer. 
3. Skaven cheap stuff is cheaper than goblin cheap stuff. Run several single giant rat packs (5 rats, 1 pack master, in a 2x3 formation) Once his manglers start heading towards things, just run a rat pack straight at the mangler. Yeah, it kills the giant rat pack, but it also kills the mangler, and considering manglers are 3x the cost of a rat pack, that’s a great trade. 
4. Units provide hard cover to other units behind them. Take two 40 strong units if Skaven slaves with slings. Deploy them side by side 20x2. Put everything else in your army behind them. If slaves die, no one cares. If he ignores the slaves and shoot at your other stuff he’s at -2 to hit, so at long range he’s hitting on 7s and can’t poison. See the statement above about short bow range. The slings are there just so you can shoot at his other blocking units like wolf riders. But, they also have the same range as his short bows. 
5. Diversify your list. If you have multiple threats, your opponent has to spread out shooting. If all you have is one big threat unit, then of course everything is going to go at it. 
6. Plague monks and rat ogres, even without armor have two benefits against  a shooting heavy list. With frenzy, they don’t care about casualties, plus if even a few get to their target they will do hella damage.

I may have to lean more pestilens

Which rules or edition are you playing