If you hit a lot of slices and pulls, your swing probably cuts across the ball from out to in. A drill for this is to set up to the ball and make a practice swing as if you were playing to a target straight out from your chest--90 degrees from your actual target. This "sideways" swing will give you the sensation that your shoulders stay closed to the target into impact. After three or four swings, hit a normal shot and try to re-create that feel.
To increase your clubhead speed, pay close attention to the relationship between your upper body and lower body, especially on the downswing. The longest hitters start down by shifting and rotating the lower body independently from the upper body: The upper body stays back as the lower body moves forward. This causes the shoulders to tilt, with the right shoulder below the left. This combination of body separation and shoulder tilt is what slings the clubhead through impact with maximum speed.