I just had a big post typed out and lost it, so now this is going to be shorter.
Killing your own units is awesome in the early game for the JE. It might make them susceptible to being rushed or having their walls attacked, but in my experience the threat of a Lioneer rush helps prevent that.
If you go first, try to get to 8 magic by the end of your second turn. If you go second, try to get to 6 magic by the end of your first turn. That means you'll probably be building at least 3 of your first 5 cards you draw as magic, and killing some of your own starting commons. You want to have enough magic to be able to summon a champion soon (especially Miti - I've still never seen an early Miti fueled by Chants defeated, and its going on 7-8 games now. I've been the victim, too [curse you Ranior and your early Miti + double CoH crap]), or at least be able to threaten summoning a champ or 2 Lioneers.
Remember that you can have no magic in your magic pile at the beginning of your attack phase and still plan to use CoG. You just have to kill something before your planned CoG unit attacks. That can be accomplished by attacking and killing another unit with your first attack, or Trampling something en route with Miti or an Elephant. I've even used Vermin to Plague something (they make an interseting combo with CoH incidentally, but I've shyed away from playing that).
Lastly, remember what Jexik said - "The JE are the kick you in the face faction." Look to setup that big turn where you just pin your opponent to the wall and kick him in the face. Like the Cloaks, they're a tricky bunch of dudes and dudettes. Try to plan out a turn where you get a Lioneer at the summoner by using a CoD or even a CoH/CoD combo. Even the double CoH on a champion is very effective (especially if it's Miti). Chant of Salvation is immensely useful in setting one of these big combos up. Use CoN when you can bypass defensive abilities with it or screw your opponent when they can use their abilities to thwart your plan. Use CoL when you have a wounded champion deep in their territory after you've made your "big play". Setting up this turn may involve baiting your opponent into moving to the right place. That is difficult.
Also, remember that CoH and CoD work on Abua Shi. Don't be afraid to CoD Abua Shi into the opposing summoners face if you can swap him with an Archer, but only if he can get the kill shot reliably. Also you can use those to get him out of trouble.