Single crystals of Cr2Ge2Te6 were studied by high-resolution capacitance dilatometry to obtain in-plane (B∥ab) and out-of-plane (B∥c) thermal expansion and magnetostriction at temperatures between 2 and 300 K and in magnetic fields up to 15 T. The anomalies in both response functions lead to the "magnetoelastic"phase diagrams and separate the paramagnetic (PM), ferromagnetic low-temperature/low-field (LTF) and aligned ferromagnetic (FM) phases. Different signs of magnetostriction anomalies as well as the evolution of thermal expansion anomalies at small fields B∥ab of different magnetic-field dependence clearly supports the scenario of an intermediate region separating PM and LTF phases in finite external in-plane magnetic fields and implies a triple point in the magnetic phase diagram. Simulations of the magnetostriction using the Stoner-Wohlfarth model for uniaxial anisotropy demonstrate that the observed quadratic-in-field behavior in the LTF phase is in line with a rotation of the spins from the preferred c direction into the ab plane. Both the LTF and the PM phase close to TC exhibit very strong pressure dependencies of the magnetization, ∂lnMab/∂pab, of several hundred %/GPa and the transition from the LTF to the FM phase strongly depends on pab (∼-280%/GPa), indicating a strong decrease in the uniaxial anisotropy under applied in-plane pressure. Our data clearly demonstrate the relevance of critical fluctuations and magnetoelastic coupling in Cr2Ge2Te6.