The antiferromagnetic semiconductor MnTe has recently attracted significant interest as a potential high-performance thermoelectric material. Its promising thermoelectric properties are due in large part to short-range magnetic correlations in the paramagnetic state, which enhance the thermopower through the paramagnon drag effect. Using magnetic pair distribution function (mPDF) analysis of neutron total scattering data, we present a detailed, real-space picture of the short-range magnetic correlation in MnTe, offering a deeper view into the paramagnon drag effect and the nature of the correlated paramagnetic state. We confirm the presence of nanometer-scale antiferromagnetic correlations far into the paramagnetic state, show the evolution of the local magnetic order parameter across the N\'eel temperature T_N=307 K, and discover a spatially anisotropic magnetic correlation length. By combing our mPDF analysis with traditional atomic PDF analysis, we also gain detailed knowledge of the magnetostructural response in MnTe. We observed a spontaneous volume contraction of nearly 1\%, the largest spontaneous magnetovolume effect reported so far for any antiferromagnetic system. The lattice strain scales linearly with the local magnetic order parameter, in contrast to the quadratic scaling observed for the conventional magnetostriction properties of this technologically relevant material. Using neutron and X-ray PDF analysis, we also investigated the local distortion on MnTe and Mn-based systems, MnS and MnO as a function of temperature. Such local distortion on MnTe increases with the rise in temperature and becomes more pronounced at 500 K.