Neuropathic pain is a type of pain that persists for a long time and becomes pathological. Additionally, the anxiodepressive disorders derived from neuropathic pain are difficult to palliate with the current treatments and need to be resolved. Then, using male mice with neuropathic pain provoked by chronic constriction of the sciatic nerve (CCI), we analyzed and compared the analgesic actions produced by three new heme oxygenase 1 (HO-1) inducers, 1m, 1b, and 1a, with those performed by dimethyl fumarate (DMF). Their impact on the anxiety- and depressive-like comportments and the expression of the inflammasome NLRP3, Nrf2, and some antioxidant enzymes in the dorsal root ganglia (DRG) and amygdala (AMG) were also investigated. Results revealed that the administration of 1m, 1b, and DMF given orally for four days inhibited the allodynia and hyperalgesia caused by CCI, while 1a merely reduced the mechanical allodynia. However, in the first two days of treatment, the antiallodynic effects produced by 1m were higher than those of 1a and DMF, and its antihyperalgesic actions were greater than those produced by 1b, 1a, and DMF, revealing that 1m was the most effective compound. At four days of treatment, all drugs exerted anxiolytic and antidepressant effects, decreased the NLRP3 levels, and increased/normalized the Nrf2, HO-1, and superoxide dismutase 1 levels in DRG and AMG. Data indicated that the dual modulation of the antioxidant and inflammatory pathways produced by these compounds, especially 1m, is a new promising therapeutic approach for neuropathic pain and related emotional illnesses.