Development of techniques that make use of synchrotron radiation (SR) and a soft x-ray monochromator enables us to investigate core-level photoexcitation and photoionization of gaseous molecules. With the linear polarization of intense soft x-rays from SR, one can observe angle-resolved fragments which help in selecting the molecular alignment or orientation at photoabsorption, since most of the fragmentation processes following the core-level photoexcitation and photoionization occur very fast. Moreover, one can combine the selection of molecular orientation or alignment with a coincidence measurement technique to perform novel measurements of the molecular core-level processes. Here, we introduce three measurement systems that we have developed: first, an angle-resolved photoion yield measurement, second, a vibrationally resolved photoelectron-photoion coincidence measurement, and third, a coincidence velocity map measurement. These measurement systems are explained along with individual applications as follows, the fragmentation dynamics of the Renner-Teller effect in the C1s → π* state of CO2 molecules, the shape resonance of vibrationally resolved core-level photoelectron angular distribution from fixed-in-space CO molecules, and the recoil frame photoelectron angular distributions of C1s electrons for C2H2 molecules with and without interference of photoelectron waves.