Cross sections and polarization transfer observables in the $^{16}$O$(p,p)$ reactions at 392 MeV were measured at several angles between $theta_{lab}=$ 0$^circ$ and 14$^circ$. The non-spin-flip (${Delta}S=0$) and spin-flip (${Delta}S=1$) strengths in transitions to several discrete states and broad resonances in $^{16}$O were extracted using a model-independent method. The giant resonances in the energy region of $E_x=19-$27 MeV were found to be predominantly excited by ${Delta}L=1$ transitions. The strength distribution of spin-dipole transitions with ${Delta}S=1$ and ${Delta}L=1$ were deduced. The obtained distribution was compared with a recent shell model calculation. Experimental results are reasonably explained by distorted-wave impulse approximation calculations with the shell model wave functions.