Stereoselective synthesis of monoterpene-based 1,2,4- and 1,3,4-oxadiazole derivatives was accomplished starting from α,β-unsaturated carboxylic acids, obtained by the oxidation of (−)-2-carene-3-aldehyde and commercially available (−)-myrtenal. 1,2,4-Oxadiazoles were prepared in two steps via the corresponding O-acylamidoxime intermediates, which then underwent cyclisation induced by tetrabutylammonium fluoride (TBAF) under mild reaction conditions. Stereoselective dihydroxylation in highly stereospecific reactions with the OsO4/NMO (N-methylmorpholine N-oxide) system produced α,β-dihydroxy 1,2,4-oxadiazoles. Pinane-based 1,3,4-oxadiazoles were obtained similarly from acids by coupling with acyl hydrazines followed by POCl3-mediated dehydrative ring closure. In the case of the arane counterpart, the rearrangement of the constrained carane system occurred with the loss of chirality under the same conditions. Stereoselective dihydroxylation with OsO4/NMO produced α,β-dihydroxy 1,3,4-oxadiazoles. The prepared diols were applied as chiral catalysts in the enantioselective addition of diethylzinc to aldehydes. All compounds were screened in vitro for their antiproliferative effects against four malignant human adherent cell lines by means of the MTT assay with the O-acylated amidoxime intermediates exerting remarkable antiproliferative action.