I've read a lot of other people's combat strategies and I will admit, those are for braver people. I tend to fight methodically, which often means slow and stealthy. With the practice, I've actually found playing on Heroic Mode now to be easier than the first time I played on Normal. I'm not the best at FPSs (a supreme understatement), so these strategies are really for my brothers and sisters that just don't have the knack for this kind of thing but still want to play.
It's almost impossible to unseat the river without trashing his ride, so don't hold out hoping to steal one. Find a good cover and take some shots when they pass. Patience is the best way to deal with a Banshee. There are several instances when they di ve at you when you step out of a door, which can be a good thing. Also, exploit a Banshee pilot's stupidity. They rarely use the Fuel Rod when you're on foot and the "stun" gun doesn't do enough damage in one pass to disable your shields. Staring them down is effective AND looks gutsy. Since Banshee's turn slowly, they have trouble avoiding a rocket headed right for 'em.