131I-MIBG Alone VS. 131I-MIBG With Vincristine and Irinotecan VS131I-MIBG With Vorinostat

Inclusion Criteria: * Patients must be \> 24 months and \< 30 years of age when registered on study. * Patients must have relapsed neuroblastoma, refractory neuroblastoma that had less than a partial response to standard treatment or persistent neuroblastoma that had at least a partial response to frontline therapy frontline therapy with \> 3 residual lesions on end-induction MIBG scan. * Patients must have evidence of MIBG uptake into tumor at ≥ one site within 4 weeks prior to entry on study and subsequent to any intervening therapy. * Patients must have adequate heart, kidney, liver and bone marrow function. Patients who have bone marrow disease must still have adequate bone marrow function to enter the study. * Patients must have a dose of unpurged peripheral blood stem cells is 2.0 x 106 viable CD34+ cells/kg available. Exclusion Criteria: * They have had previous I-131 MIBG therapy * They have other medical problems that could get much worse with this treatment. * They are pregnant or breast feeding. * They have a history of a venous or arterial thrombosis that was not associated to a central line. * They have active infections such as hepatitis or fungal infections. * They have active diarrhea. * They have had an allogeneic stem cell transplant (received stem cell from someone else) * They can't cooperate with the special precautions that are needed for this trial.