Antibacterial and antioxidant properties of the leaves and stem essential oils (EOs) of Jatropha gossypifolia and their efficacies against infectious and oxidative stress diseases were studied in vitro. The EOs obtained using Clevenger modified apparatus were characterized by high resolution GC-MS, while their antioxidant and antibacterial properties were examined by spectrophotometric and agar diffusion techniques, respectively. The EOs exhibited strong antibacterial activity against Escherichia coli, Enterococcus faecium, and Staphylococcus aureus. The stem essential oil (SEO) was more active than the leaf essential oil (LEO) against test bacteria with minimum inhibition concentration (MIC) ranging from 0.025 to 0.05 mg/mL and the LEO from 0.05 to 0.10 mg/mL. The SEO was bactericidal at 0.025 and 0.05 mg/mL against S. aureus and E. faecium, respectively, and the LEO was bacteriostatic against the three bacteria at 0.05 and 0.10 mg/mL. The SEO IC50 (0.07 mg/mL) showed that the antiradical strength was superior to LEO (0.32 mg/mL) and β-carotene (1.62 mg/mL) in scavenging 2, 2-diphenyl-1-picrylhydrazyl radicals (DPPH•). The oils effectively reduced three other oxidants to neutral molecules in concentration dependent manner. Findings from this study suggest that, apart from the traditional uses of the plant extracts, the EOs have strong bioactive compounds with noteworthy antibacterial and antiradical properties and may be good candidates in the search for lead compounds for the synthesis of novel potent antibiotics.