Your ult makes people run away from you, not in a random direction. So if you can target your ult just very slightly behind the enemy champion, they'll run away from you, and hopefully right into your team. You can make this more effective by casting E right before you ult, so as soon as your ult is over and they've started running toward your team, you push them even further out of position.
E's movement buff affects your AD, so you can usually get one Q off with the boosted AD before spending the movement buff on an attack.
E also gives you an attack range boost, allowing you to hop small walls if your target is right on the other side.
W heals you for all damage dealt to enemies inside the field, not just your own damage, so after all the CD nerfs, you need to make sure to use it in the thick of the teamfight so you can heal for all the damage your team is doing and not just your own.
I reject your reality and substitute my own! -Adam Savage, The Mythbusters