We present measurements of diffuse interstellar $H_2$ absorption lines in the continuum spectra of 10 early-type stars. The data were observed with the Berkeley Extreme and Far-Ultraviolet Spectrometer (BEFS) of the ORFEUS telescope on board the ORFEUS-SPAS I and II space-shuttle missions in 1993 and 1996, respectively. The spectra extend from the interstellar cutoff at 912 $AA$ to about 1200 $AA$ with a resolution of ~ 3000 and statistical signal-to-noise ratios between 10 and 65. Adopting Doppler broadening velocities from high-resolution optical observations, we obtain the $H_2$ column densities of rotational levels J" = 0 through 5 for each line of sight. The kinetic temperatures derived from J" = 0 and 1 states show a small variation around the mean value of 80 K, except for the component toward HD 219188, which has a temperature of 211 K. Based on a synthetic interstellar cloud model described in our previous work, we derive the incident UV intensity IUV and the hydrogen density $n_H$ of the observed components to be -0.4 $leq$ log $I_{UV}leq2.2$ and $6.3{leq}n_H2500cm^{-3}$, respectively.