In this paper, we study various types of exponents of oscillation (upper or lower, strong or weak) of non-strict signs, zeros, and roots of non-zero solutions of linear homogeneous differential equations of the third order with continuous and bounded coefficients on the positive semi-axis. A nonzero solution of a linear homogeneous equation cannot be zeroed due to the existence and uniqueness theorem. Therefore, the spectra of all the listed exponents of oscillation (i.e. their sets of values on nonzero solutions) consist of one zero value.