The aim of the study was to investigate the comparative effects of different combinations of sodium butyrate (SB), medium-chain fatty acids (MCFAs), and omega-3 polyunsaturated fatty acids (n-3 PUFAs) on the reproductive performances of sows, as well as on the biochemical parameters, oxidative statuses, and intestinal health of the sucking piglets. A total of 30 sows were randomly allocated to five treatments: (1) control diet (CON); (2) CON with 1 g/kg of coated SB and 7.75 g/kg of coated MCFAs (SM); (3) CON with 1 g/kg of coated SB and 68.2 g/kg of coated n-3 PUFAs (SP); (4) CON with 7.75 g/kg of coated MCFAs and 68.2 g/kg of coated n-3 PUFAs (MP); (5) CON with 1 g/kg of coated SB, 7.75 g/kg of coated MCFAs and 68.2 g/kg of coated n-3 PUFA (SMP). The results showed that sows fed the SP, MP, and SMP diets had shorter weaning-to-estrus intervals than those fed the CON diet (p < 0.01). The piglets in the SM, SP, and MP groups showed higher increases in the plasma catalase and glutathione peroxidase activities than those of the CON group (p < 0.01). The diarrhea incidence of piglets in the SM, SP and SMP groups was lower than that of piglets in the CON group (p < 0.01). Additionally, the addition of SM, SP, MP, and SMP to the sow diets increased the contents of immunoglobulin A, immunoglobulin G, fat, and proteins in the colostrum (p < 0.01), as well as the plasma total superoxide dismutase activities (p < 0.01) in the suckling piglets, whereas it decreased the mRNA expressions of tumor necrosis factor-α, interleukin-1β, and toll-like receptor 4 in the jejunum mucosa of the piglets. The relative abundances of Prevotella, Coprococcus, and Blautia in the colonic digesta of the piglets were increased in the SM group (p < 0.05), and the relative abundances of Faecalibacterium increased in the SMP group (p < 0.05), compared with the CON group. The relative abundances of Collinsella, Blautia, and Bulleidia in the MP group were higher than those in the CON group (p < 0.05). Collectively, dietary combinations of fatty acids with different chain lengths have positive effects on the growth performances and intestinal health of suckling piglets.