Straight of grain refers to the weave of the fabric. See Cross Grain
A straight stitch foot can be used for machine piecing.
String piecing refers to a sewing technique where scraps of fabrics are sewn together into sections. Shapes are then cut out of these sections. The shapes are then sewn together in a traditional pattern.
Strip piecing is a quick sewing and rotary cutting technique. Long strips of fabric are cut using a rotary cutter. They are sewn together and then cut into smaller units. These smaller units are then sewn together again to form traditional quilts.