We have experimentally investigated nanostructures consisting of free-standing microtubes with diameters in the micrometer range fabricated by rolling-up InGaAs/GaAs bilayers grown by molecular-beam epitaxy on a GaAs substrate. The formation of the microtubes is powered by the built-in strain in the InGaAs layer and they develop after releasing the bilayer structure from the substrate by selective etching. Through micro-Raman spectroscopy we were able to detect the residual strain of the microtube, which results in a frequency shift of phonon modes measured on the tube as compared with reference unstrained material. We developed a simple elastic model to describe the measured phonon frequency shifts, from which we estimate the strain status of the microtube. Results demonstrate the power of Raman spectroscopy as a diagnostic tool for engineering of strain-driven self-positioning microelectromechanical systems.