When magnetic field is applied to metals and semimetals quantum oscillations appear as individual Landau levels cross the Fermi level. Quantum oscillations generally do not occur in superconductors (SC) because magnetic field is either expelled from the sample interior or, if strong enough, drives the material into the normal state. In addition, elementary excitations of a superconductor-Bogoliubov quasiparticles-do not carry a well-defined electric charge and therefore do not couple in a simple way to the applied magnetic field. We predict here that in Weyl superconductors certain types of elastic strain have the ability to induce chiral pseudomagnetic field, which can reorganize the electronic states into Dirac-Landau levels with linear band crossings at low energy. The resulting quantum oscillations in the quasiparticle density of states and thermal conductivity can be experimentally observed under a bending deformation of a thin film Weyl SC and provide new insights into this fascinating family of materials.