Driver and woods push right, irons go left.
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From your description, you have an in-to-out swing with both driver and irons, ie. you swing out to the right. With the irons, you're getting the face square to the target line at impact, so the ball starts out straight with draw spin on it. With the driver, your face is open (to the target) at impact and pointing down the line of your swing path, so the ball starts right and has no curve.
The simplest thing to try would be altering your setup. With the irons, try moving the ball back slightly in your stance and consciously opening the face (to the target) slightly at address. If you were aiming at a pin in the dead center of the green, get your club face pointing to the right fringe at setup. You want the ball to initially push right and then draw back toward the target. With the driver, the opposite is true, since you want less push and more (any!) draw. So you need the club face less open (to the target) at impact. Try moving the ball up to your left instep and see what happens.
Edited by Stretch - 7/30/11 at 10:40am