Honestly the biggest threat in a khorne demon army will be the cannons, demon princes, and bloodthirster. Cannons you either need to take care of quickly, or build a lists that won't be too bothered by them.
Screams can take out the DP or Great Demon, a tooled up VL could also do rather well. One thing to keep in mind, though scary the Demon Army doesn't have high saves, so a lot of low strength attacks over a period of time can bring down the 'Thirster or DP. Take champions in every unit you can, so as to challenge out the big scary guys to buy you extra rounds.
My personal suggestion try to tie up the DP/ 'THirster, gun for the other points. Blood Crushers put out a decent amount of attacks but have no staying power due to low armor saves. Bloodletters are as squishy as elves. These are your "easy" points. Keep in mind bloodcrushers and blood letters have killing blow.
Khorne demons will almost never be frenzied. The only way for them to frenzy is with a special character, which also frenzies you, or with a herald taking an over pointed loci, which doesn't often happen. If you do run into a loci running herald, just kill the herald but regulating attacks on it, boom, problem solved.
I agree with Najo that poison attacks will do well. I also would rate the Hexwraiths, the most maneuverable things in the army are the characters, avoid them and the cannons you should be able to continually run through the support stuff to devastating effect.
One last piece of advice, don't send your Vampire out of a unit if at all possible, the Reign of Chaos table targets each unit not in combat, and inevitably the turn your Vamp is on its own it will get hit and killed by something! Plus cannons lol!
Good luck
