We study the interplay between strain and composition during the elementary process steps which allow the fabrication of strained ultra-thin SiGe layers on insulators from a Silicon-On-Insulator (SOI) substrate by the Ge condensation technique. Strain maps with subnanometer resolution and high precision are obtained using the dark-field electron holography technique. We confirm that two basic mechanisms drive the final composition of the top layer, namely Ge injection during oxidation and Si/Ge interdiffusion, both thermally activated. We show that during this process the observed strain results from the out-of-plane relaxation of the stress generated by the substitution of Si by Ge atoms in the Si lattice, rigidly bounded to the underlying buried oxide.