First...I'll second that you shouldn't bother to take swordsman. When my SoKs can soak up attacks from Stygian swordmen, it spells disaster for them...and SoK have the worst armor.
Anyway, tips.
First, have Starved in the front. They're crazy, and running them up ahead of the rest of the Stygies will force your opponent to either rush forward to try to get the chare, or come to a halt sooner to wait and hope you don't kill his models on the Leap.
Second, always have your Axemen run up ahead of the Spearmen. Axemen do nasty damage if you run out of base-to-base contact room, Spearmen have that 1" reach.
Third, make sure you get the right individuals for the right effect. Great Warriors are relatively cheap and are great for speedy flankers. A Tree Devil makes a great suicide assassin. Overall, I highly reccommend the Guardians. Those things are brutal, though slow.
Finally, make good use of spells. The Priestess has the widest variety of most viscious spells, use them.