The reaction mechanism of deep-inelastic multinucleon transfer processes in the $^{16}$O+$^{27}$Al reaction at an incident $^{16}$O energy ($E_{rm lab}=134$ MeV) substantially above the Coulomb barrier has been studied both experimentally and theoretically. Elastic-scattering angular distribution, total kinetic energy loss spectra and angular distributions for various transfer channels have been measured. The $Q$-value- and angle-integrated isotope production cross sections have been deduced. To obtain deeper insight into the underlying reaction mechanism, we have carried out a detailed analysis based on the time-dependent Hartree-Fock (TDHF) theory. A recently developed method, TDHF+GEMINI, has been applied to evaluate production cross sections for secondary products. From a comparison between the experimental and theoretical cross sections, we find that the theory qualitatively reproduces the experimental data. Significant effects of secondary light-particle emissions are demonstrated. Possible interplay between fusion-fission, deep-inelastic, multinucleon transfer and particle evaporation processes are discussed.