The nuclides 92Mo, 98Mo, and 100Mo have been studied in photon-scattering experiments by using bremsstrahlung produced at an electron energy of 6 MeV at the ELBE accelerator of the Forschungszentrum Rossendorf and at electron energies from 3.2 to 3.8 MeV at the Dynamitron accelerator at the University of Stuttgart. Six dipole transitions in 98Mo and 19 in 100Mo were observed for the first time in the energy range from 2 to 4 MeV. The experimental results are compared with predictions of the shell model and with predictions of the quasiparticle random-phase approximation (QRPA) in a deformed basis. The latter show significant contributions of isovector-orbital and isovector-spin vibrations. The change of the magnetic dipole strength in the isotopic chain of the even-mass isotopes from 92Mo to 100Mo is discussed. The calculations within the QRPA are extrapolated to the particle-separation energies to estimate the possible influence of M1 strength on the stability of the nuclides against photodissociation in cosmic scenarios.