A wall construction system includes multiple block types that interfit with one another to form walls in a staggered arrangement. Block types include jamb blocks having front and back surfaces, a planar surface on a first end, and a second side having a projecting surface or a receiving surface configured to mate with the projecting surface. The jamb block includes a top mating surface and a bottom mating surface configured to mate with the top mating surface. Webs extend from the front surface to the back surface to form voids. A multi-directional elevation is formed over a void adjacent the planar surface to permit stacking of blocks in two orientations. Other block types include a half jamb block having a web to form a void and a planar surface, and a web stretcher having a projecting surface on one end and a receiving surface on another end.