Nanoparticles may contain unusual forms of structural disorder that can substantially modify materials properties and thus cannot solely be considered as small pieces of bulk material. We have developed a method to quantify intermediate-range order in 3.4-nanometer-diameter zinc sulfide nanoparticles and show that structural coherence is lost over distances beyond 2nanometers. The zinc-sulfur Einstein vibration frequency in the nanoparticles is substantially higher than that in the bulk zinc sulfide, implying structural stiffening. This cannot be explained by the observed 1% radial compression and must be primarily due to inhomogeneous internal strain caused by competing relaxations from an irregular surface. The methods developed here are generally applicable to the characterization of nanoscale solids, many of which may exhibit complex disorder and strain.