We studied crystal structures in a monolayer consisting of anisotropic branched colloidal (nano)octapods. Experimentally, octapods were observed to form a monolayer on a substrate with a square-lattice crystal structure by drop-casting and fast evaporation of solvent. The experimental results were analyzed by Monte Carlo simulations using a hard octapod model consisting of four interpenetrating spherocylinders. We confirmed by means of free-energy calculations that crystal structures with a (binary-lattice) square morphology are indeed thermodynamically stable at high densities. The effect of the pod length-to-diameter ratio on the crystal structures was also considered and we used this to constructed the phase diagram for these hard octapods. In addition to the (binary-lattice) square crystal phase, a rhombic crystal and a hexagonal plastic-crystal (rotator) phase were obtained. Our phase diagram may prove instrumental in guiding future experimental studies.