Actually, the plot you show is modulus, which is stiffness, not strength. "E" is stiffness in tension/compression and "G" is shear stiffness, usually expressed in lbs/sqin. Strength follows roughly the same trend, though. At 15 degrees skew, strength of bi-directional glass cloth drops to about 38% of that at 0 degrees and at 45 degrees it is about 19%. I got this from a laminate analysis program called Compro. If you go with a quasi-isotropic laminate, which is what you have if you have equal numbers of 0 and 45 degree plies, the strength is roughly equal in all directions and is about 72% of a 0 degree ply.
Composites hate asymmetry. That single 15 degree ply is really down on strength, however if you balance it with a ply at -15 degrees, strength goes up from 38% to 95%. This brings up an important point and that is that the 38% number is artificially low. It assumes that the ply acts by itself, but in reality the wood core helps to balance it. Strength would never be as bad as 38% in the real life application.

Ideally, each facing of a sandwhich should be symmetric, so a 15/-15/-15/15 laminate is better than a 15/-15 laminate. Also, to get the most performance from the sandwich, the inner and outer facings should be the same and symmetric about the core CL.