High-Dose Chemotherapy With or Without Total-Body Irradiation Followed by Autologous Stem Cell Transplant in Treating Patients With Hematologic Cancer or Solid Tumors

Inclusion Criteria: * Histologically confirmed diagnosis of malignant hematologic disorders, amyloidosis or solid tumor malignancy * Recurrent or refractory disease or disease at high risk for recurrence * Hodgkin Disease (HL): Relapsed or refractory disease after chemotherapy with a minimum of one standard regimen * Non-Hodgkin Lymphoma (NHL): (Low, Intermediate or High Grade) Relapsed or refractory disease after chemotherapy with at least one standard regimen or first complete remission (CR) lymphoblastic or small, non-cleaved cell lymphoma at high risk of relapse by high International Prognostic Index (IPI) Score * Acute Myeloid Leukemia (AML): Low or High Risk disease in first or second CR or greater in patients in whom the risks of an allogeneic transplant outweigh the benefits * Acute Lymphoblastic Leukemia (ALL): Low or high risk disease in first or second CR in whom the risks of an allogeneic transplant outweigh the benefits * Multiple Myeloma (MM): Low or high risk in first or greater response (stable disease or better) or for responding patients at first progression * Other Malignant Lymphoproliferative Disorders: (chronic lymphocytic lymphoma \[CLL\], Waldenstroms macroglobulinemia, relapsed or refractory disease after first-line chemotherapy * Amyloidosis: primary or previously treated * Solid Tumors: Testicular cancer patients who have relapsed disease or primary progressive disease which is responding to salvage therapy; relapsed or advanced-stage newly diagnosed neuroblastoma (NBL) or small round blue cell tumors (SRBCT) in patients 30 years of age; other patients with solid tumors who have recurred following conventional treatment or are at high risk for relapse, and demonstrate chemosensitivity * Patients with malignancies who would be treated with an autologous stem cell transplant but have a syngeneic donor; a syngeneic donor would be considered to have the same risk as an autologous stem cell transplant patient * Performance status 0-2 (Karnofsky performance status \[KPS\] \>= 70%); patients with amyloidosis or MM with decreased KPS due to disease are eligible * Life expectancy \> 2 months * Pulmonary function tests; diffusing capacity of the lung for carbon monoxide (DLCO) or diffusing volume of the alveolar volume (DLVA) \>= 50% predicted; DLCO to be corrected for hemoglobin and/or alveolar ventilation * Cardiac ventricular ejection fraction \>= 50% by radionuclide ventriculogram or echocardiogram * Bilirubin \< 3 x normal * Alkaline phosphatase, serum glutamic oxaloacetic transaminase (SGOT) \< 3 x normal * Calculated creatinine clearance \< 40 cc/min by the modified Cockcroft-Gault formula for adults or the Schwartz formula for pediatrics * Glomerular filtration rate by renal scan for neuroblastoma patients, to determine dosing parameters * Positive cytomegalovirus (CMV) immunoglobulin M (IgM) and/or positive hepatitis serologies demonstrating infection will require an Infectious Disease consult and subsequent clearance * Any active infection will require an Infectious Disease consult and subsequent clearance * Peripheral Blood Counts of polymorphonuclear neutrophil (PMN) \> 1500/uL * Platelet (Plt) \> 75,000/uL * Prior to stem cell storage: * No radiation within three weeks before stem cell harvest * Bone marrow may be used in conjunction with blood progenitor cells * Hematologic Malignancy patients with human immunodeficiency virus (HIV) positivity but on appropriate anti-retroviral therapy may go autotransplant with the following laboratory tests; (CD4+ cell count \> 75 cells per microliter and HIV copy number \< 100,000 per microliter and with Infectious Disease clearance * Acute Leukemia, HL, NHL, MM and Solid Tumor patients must have received 2 cycles of chemotherapy followed by disease-specific restaging prior to mobilization and collection of stem cells; small round blue cell tumor patients must have received either standard therapy or surgical intervention; the disease status and response to therapy must be known prior to transplant to establish the disease status at transplant; amyloidosis patients may proceed to BMT without receiving chemotherapy * No serious organ dysfunction unless it is caused by the underlying disease, exclusion criteria include the following: * Uncontrolled or severe cardiovascular disease, including recent (\< 6 months) myocardial infarction, congestive heart failure, symptomatic angina, life-threatening arrhythmia or hypertension * Active bacterial, viral, or fungal infection * Active peptic ulcer disease * Uncontrolled diabetes mellitus * No serious medical or psychiatric illness * Not pregnant * No psychiatric conditions which would prevent delivery of care; psychology clearance is necessary * Allogeneic BMT not possible, or not desirable * Age \> 65 years * No compatible donor identified * Estimated risk of graft vs. host disease complications greater than risk of recurrence after autologous BMT * Adequate bone marrow or blood stem cell dose obtained: * For blood stem cells: total CD 34+ \>= 2 x 10\^6/kg or if unable to collect this dose, a total nucleated cell bone marrow dose of \>= l x 10\^8/kg