• Males or females

• 18 to 99 years of age

• Histologically confirmed cutaneous melanoma by historical pathology report review, clinical Stage I-III (Cohort #1), or Stage IV (Cohort #2) cutaneous melanoma

• At least one, biopsy-proven, palpable melanoma tumor deposit suitable for intralesional injection measuring ≥ 1 cm by digital caliper (with digital photography documentation) or ultrasound (with ultrasound image documentation)

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1

• Absolute neutrophil count (ANC) \>= 1.5 x 10\^3/mm\^3 (drawn at or not more than 30 days prior to the screening visit)

• Hemoglobin (Hgb) \>= 9 g/dL (drawn at or not more than 30 days prior to the screening visit)

• Platelet count \>= 100 x 10\^3/mm\^3 (drawn at or not more than 30 days prior to the screening visit)

• Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN) or =\< 5 x ULN in patients with liver metastases (Cohort 2 only) (drawn at or not more than 30 days prior to the screening visit)

• Prothrombin time =\< 1.5 x ULN (drawn at or not more than 30 days prior to the screening visit)

• Total bilirubin =\< 1.5 x ULN (unconjugated bilirubin of \< 3 x ULN for patients with known Gilbert syndrome) (drawn at or not more than 30 days prior to the screening visit)

• Creatinine clearance of \>= 50 ml/min by Cockcroft-Gault equation (drawn at or not more than 30 days prior to the screening visit)

• Women of childbearing potential (WOCBP) must agree to use effective contraceptive methods from screening until at least:

‣ Cohort 1: 14 days after the surgical resection for subjects in Cohort 1

⁃ Cohort 2:

• Nivolumab: 5 months after the last dose of either nivolumab or intralesional Flucelvax, whichever is later

∙ Pembrolizumab: 4 months after the last dose of either pembrolizumab or intralesional Flucelvax, whichever is later

∙ Ipilimumab: 3 months after the last dose of either ipilimumab or intralesional Flucelvax, whichever is later

∙ Relatlimab + nivolumab (marketed under the trade name Opdualag): 5 months after the last dose of either Opdualag or intralesional Flucelvax, whichever is later.

∙ Combination ipilimumab with other checkpoint inhibitor: Whichever is later:

‣ 3 months after the last dose of either ipilimumab or intralesional Flucelvax

⁃ Above-bulleted recommendation for nivolumab or pembrolizumab

• Non-childbearing potential is defined as a woman who meets either of the following criteria: a) postmenopausal state defined as no menses for 12 months without an alternative medical cause, or b) documented hysterectomy, bilateral tubal ligation, or bilateral oophorectomy

• Effective contraception methods are defined as one of the following:

‣ True abstinence, defined as refraining from heterosexual intercourse, when this is in line with the preferred and usual lifestyle of the subject

⁃ Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods), declaration of abstinence for the duration of a trial, and withdrawal are not acceptable methods of contraception

⁃ Condoms and spermicide

⁃ Diaphragm and spermicide

⁃ Oral or implanted hormonal contraceptive

⁃ An intra-uterine device

• WOCBP must have a negative pregnancy test (serum or urine)