The present study examined the effects of dietary supplementation with extracts of pomegranate (Punica granatum) and onion (Allium cepa), either encapsulated in cyclodextrin (POMALCD group) or in an aqueous (POMALAQ group) form, on breast meat, thigh meat, and liver composition, oxidative stability, cellular signaling pathways, and the gene expression of certain hepatic genes. The results showed that breast and thigh meat contained significantly (p < 0.05) higher moisture content in the group with the aqueous extract, compared to the control and POMALCD groups. Moreover, the protein content was significantly (p < 0.05) higher in the thigh and liver samples of the treated groups in comparison to the control. The iron-induced challenge deteriorated (p < 0.001) the lipid and protein oxidative status of the control group, whereas both supplemented groups showed considerable tolerance in all tissues. The supplementation of pomegranate and onion extracts mitigated or maintained heat shock protein (HSP) levels and elevated (p < 0.05) the Bcl-2/Bad ratio in thigh and breast meat, whereas mitogen-activated protein kinase (MAPK) activation was modulated at a lower rate. After normalization to β-actin expression, quantitative real-time PCR analysis revealed a significant (p < 0.05) induction in the expression of MTR and MSRB1 genes in the liver of the supplemented groups. No differences were observed for the TAT, SMS, and BHMT genes. In conclusion, dietary mixtures of herbal extracts with pomegranate and onion improved protein and lipid oxidative stability in meat, enhanced the hepatic energy status, and exerted ameliorative effects on stress-related proteins. The encapsulated extract of pomegranate and onion, using cyclodextrin as a carrier, appeared to reduce lipid oxidation to a greater extent than the aqueous extract. In contrast, the aqueous extract exhibited higher total antioxidant capacity (TAC) values and provided better protection against protein carbonyl formation.