The reaction of sydnone-derived 3-aryl-5-methyl-1,3,4-oxadiazol-2(3H)-ones with thiourea and α-bromoacetophenone derivatives in the presence of a catalytic amount of TiCl4 produces 2-aryl-4-(4-aryl-1,3-thiazol-2-yl)-5-methyl-2,4-dihydro-3H-1,2,4-triazol-3-ones. The title compounds were screened for their antibacterial and antifungal activity. The toxicity of the compounds was evaluated in terms of mutagenicity, tumorigenicity, and reproductive effects. The drug-relevant properties (ClogP, drug-likeness, and drug score) were calculated, and the structure–activity relationship was discussed.