Irinotecan Hydrochloride, Temozolomide, and Dinutuximab With or Without Eflornithine in Treating Patients With Relapsed or Refractory Neuroblastoma

Inclusion Criteria: * Patients must have had histologic verification of neuroblastoma or ganglioneuroblastoma or demonstration of neuroblastoma cells in the bone marrow with elevated urinary catecholamines (i.e. \> 2 x upper limit of normal \[ULN\]), at the time of initial diagnosis. * For the purposes of this study, aggressive multidrug chemotherapy is defined as chemotherapy including 2 or more agents that must include an alkylating agent and a platinum-containing compound as intended to treat high-risk disease. The doses of chemotherapy must be comparable to those used in frontline high-risk neuroblastoma therapies (examples include A3973, ANBL0532, ANBL09P1, ANBL12P1, and ANBL1531). Patients must have ONE of the following: * First episode of recurrent high-risk disease following completion of aggressive multi-drug frontline high-risk therapy. * First episode of progressive high-risk disease during aggressive multi-drug frontline therapy. * Primary resistant/refractory disease (less than partial response by International Neuroblastoma Response Criteria \[INRC\]) detected at the conclusion of at least 4 cycles of aggressive multidrug induction chemotherapy on or according to a high-risk neuroblastoma protocol (examples include A3973, ANBL0532, ANBL09P1, ANBL12P1, ANBL1531, etc.). * Patients must have at least ONE of the following at the time of enrollment: * Measurable tumor on magnetic resonance imaging (MRI) or computed tomography (CT) scan. Measurable is defined as \>= 10 mm in at least one dimension on spiral/helical CT that is metaiodobenzylguanidine (MIBG) avid or demonstrates increased fludeoxyglucose F-18 (FDG) uptake on positron emission tomography (PET) scan. * MIBG-avid lesion detected on MIBG scan with positive uptake at a minimum of one site. This site must represent disease recurrence after completion of therapy, progressive disease on therapy, or refractory disease during induction. * Patients with resistant/refractory soft tissue disease that is not MIBG avid or does not demonstrate increased FDG uptake on PET scan must undergo biopsy to document the presence of viable neuroblastoma. Biopsy is not required for patients who have a new site of soft tissue disease (radiographic evidence of disease progression) regardless of whether progression occurs while receiving therapy or after completion of therapy. * Patients with bone marrow disease only will be eligible if they have more than 5% disease involvement (documented neuroblastoma cells) in at least one sample from bilateral bone marrow biopsies. * Note: Patients with elevated catecholamines (i.e. \> 2 x ULN) only are NOT eligible for this study. * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2. Use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age. * Primary refractory/resistant patients must have received at least 4 cycles of frontline high-risk chemotherapy. Frontline therapy may also have included surgery, chemotherapy, autologous stem cell transplantation (SCT) +/- MIBG, immunotherapy, radiotherapy, and retinoids but must NOT have received second line therapy for resistant/refractory, relapsed, or progressive disease. Patients who received intensified therapy for poor induction response or refractory disease (e.g. MIBG) will be considered to have received second line therapy and will not be eligible. * At least 14 days must have elapsed since completion of myelosuppressive therapy. * Anti-cancer agents not known to be myelosuppressive (e.g. not associated with reduced platelet or absolute neutrophil count \[ANC\] counts): \>= 7 days after the last dose of agent. * Antibodies: \>= 21 days must have elapsed from infusion of last dose of antibody, and toxicity related to prior antibody therapy must be recovered to grade =\< 1. * No interim time prior to study entry is required following prior radiation therapy (RT) for non-target lesions. However, patients must not have received radiation for a minimum of 4 weeks prior to study entry at the site of any lesion that will be identified as a target lesion to measure tumor response. Lesions that have been previously radiated cannot be used as target lesions unless there is radiographic evidence of progression at the site following radiation or a biopsy done following radiation shows viable neuroblastoma. Palliative radiation while on study is not permitted. * Patients are eligible \>= 6 weeks after autologous stem cell transplants or stem cell infusions (including stem cell infusions given as supportive care following 131 I-MIBG therapy) as long as hematologic and other eligibility criteria have been met. * Patients are eligible \>= 6 weeks after therapeutic 131 I-MIBG provided that all other eligibility criteria are met. * Subjects who have previously received anti-GD2 monoclonal antibodies with or without retinoids for biologic therapy are eligible unless they have had progressive disease while receiving prior anti-GD2 therapy or progressed/relapsed within 3 months of receiving anti-GD2 therapy. However, eligible patients may NOT have received anti-GD2 monoclonal antibodies in combination with chemotherapy. * Subjects who have received autologous marrow infusions or autologous stem cell infusions that were purged using monoclonal antibody linked to beads are eligible. * Subjects who have previously received DFMO are eligible for this study provided they have not had progressive disease while receiving DFMO or progressed/relapsed within 3 months of completing DFMO. * Patients must not have received long-acting myeloid growth factors (e.g. pegfilgrastim) within 14 days of entry on this study. Seven days must have elapsed since administration of a short-acting myeloid growth factor. * For patients with solid tumors (without marrow involvement) including status post SCT: peripheral absolute neutrophil count (ANC) \>= 750/uL (within 7 days prior to enrollment). * For patients with solid tumors (without marrow involvement) including status post SCT: platelet count \>= 75,000/uL (transfusion independent) (within 7 days prior to enrollment). * Patients known to have bone marrow involvement with neuroblastoma are eligible provided that minimum ANC and transfusion independent platelet count criteria are met (as above). However, these patients are not evaluable for hematological toxicity. * Creatinine clearance or radioisotope GFR \>= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows: * 1 to \< 2 years (male 0.6 mg/dL, female 0.6 mg/dL) * 2 to \< 6 years (male 0.8 mg/dL, female 0.8 mg/dL) * 6 to \< 10 years (male 1 mg/dL, female 1 mg/dL) * 10 to \< 13 years (male 1.2 mg/dL, female 1.2 mg/dL) * 13 to \< 16 years (male 1.5 mg/dL, female 1.4 mg/dL) * \>= 16 years (male 1.7 mg/dL, female 1.4 mg/dL) (within 7 days prior to enrollment). * Total bilirubin =\< 1.5 x ULN for age (within 7 days prior to enrollment). * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 5.0 x ULN for age (=\< 225 U/L). For the purpose of this study, the ULN for SGPT is 45 U/L (within 7 days prior to enrollment). * Shortening fraction of \>= 27% by echocardiography (ECHO) (within 7 days prior to enrollment). * Ejection fraction of \>= 50% by ECHO or gated radionuclide study (within 7 days prior to enrollment). * No evidence of dyspnea at rest, no exercise intolerance, no chronic oxygen requirement, and room air pulse oximetry \> 94% if there is a clinical indication for pulse oximetry. Normal pulmonary function tests in patients who are capable of cooperating with testing (including diffusion capacity of the lung for carbon monoxide \[DLCO)\] are required if there is a clinical indication for determination. For patients who do not have respiratory symptoms, full pulmonary function tests (PFTs) are NOT required. * Patients with a history of central nervous system (CNS) disease must have no clinical or radiological evidence of active CNS disease at the time of study enrollment. * Patients with seizure disorders may be enrolled if seizures are well controlled on anti-convulsants. * CNS toxicity =\< grade 2. Exclusion Criteria: * Men and women of childbearing potential and their partners must agree to use adequate contraception while enrolled on this study. Based on the established teratogenic potential of alkylating agents, pregnant women will be excluded from this study. Because of potential risks to breastfed infants due to drug metabolites that could be excreted in breast milk, female patients who are lactating must agree to stop breastfeeding or will otherwise be excluded from this study. Females of childbearing potential must have a negative pregnancy test to be eligible for this study. * Patients with only elevated catecholamines (i.e. \> 2 x ULN) are NOT eligible for this study. * Patients must have been off pharmacologic doses of systemic steroids for at least 7 days prior to enrollment. Patients who require or are likely to require pharmacologic doses of systemic corticosteroids while receiving treatment on this study are ineligible. The only exception is for patients known to require 2 mg/kg or less of hydrocortisone (or an equivalent dose of an alternative corticosteroid) as premedication for blood product administration in order to avoid allergic transfusion reactions. The use of conventional doses of inhaled steroids for the treatment of asthma is permitted, as is the use of physiologic doses of steroids for patients with known adrenal insufficiency. Patients on any other immunosuppressive medications (e.g. cyclosporine, tacrolimus) are not eligible. * Patients must not have received prior treatment with irinotecan and temozolomide. * Patients must not have received enzyme-inducing anticonvulsants including phenytoin, phenobarbital, or carbamazepine for at least 7 days prior to study enrollment. Patients receiving non-enzyme inducing anticonvulsants such as gabapentin, valproic acid, or levetiracetam will be eligible. * Patients who have received drugs that are strong inducers or inhibitors of CYP3A4 within 7 days prior to study enrollment are not eligible. * Patients must not have been diagnosed with myelodysplastic syndrome or with any malignancy other than neuroblastoma. * Patients with symptoms of congestive heart failure are not eligible. * Patients must not have \>= grade 2 diarrhea. * Patients who are unable to tolerate oral/nasogastric/gastrostomy medications will not be eligible for this trial. Additionally, patients with significant malabsorption will not be eligible for this trial. * Patients must not have uncontrolled infection. * Patients with a history of grade 4 allergic reactions to anti-GD2 antibodies or reactions that required permanent discontinuation of the anti-GD2 therapy are not eligible. * Patients with a significant intercurrent illness (any ongoing serious medical problem unrelated to cancer or its treatment) that is not covered by the detailed exclusion criteria and that is expected to interfere with the action of study agents or to significantly increase the severity of the toxicities experienced from study treatment are not eligible.