This study reveals the existence of oxidative stress (reactive oxygen species (ROS)) in non-nervous organs and tissues in multiple sclerosis (MS) by means of a model of experimental autoimmune encephalomyelitis (EAE) in rats. This model reproduces a similar situation to MS, as well as its relationship with intestinal microbiota starting from the changes in bacterial lipopolysaccharide levels (LPS) in the outer wall of the gram-negative bacteria. Finally, the administration of extra-virgin olive oil (EVOO), hydroxytirosol (HT), and oleic acid (OA) exert beneficial effects. Twenty-five Dark Agouti two-month-old male rats, weighing around 190 g, were distributed into the following groups: Control, EAE (experimental autoimmune encephalomyelitis group), EAE + EVOO, EAE + HT, and EAE + OA. The glutathione redox system with the EAE was measured in heart, kidney, liver, and small and large intestines. The LPS and the correlation with oxidative stress in the small and large intestines were also investigated. The results showed that (1) the oxidative damage in the EAE model affects non-nervous organs and tissues; (2) The LPS is related to inflammatory phenomena and oxidative stress in the intestinal tissue and in other organs; (3) The administration of EVOO, HT, and OA reduces the LPS levels at the same time as minimizing the oxidative damage; (4) EVOO, HT, and OA improve the disease’s clinical score; and (5) on balance, EVOO offers a better neuroprotective effect.