Wilm's Tumor 1 Protein Vaccine to Treat Cancers of the Blood

* INCLUSION CRITERIA: Inclusion Criteria: Patient (i.e., transplant recipient) Age greater than 1 year and less than 75 years. One of the following Wilm's Tumor 1 (WT1)-expressing hematologic malignancies: 1. Acute lymphocytic leukemia (ALL), less than or equal to 25 percent marrow blasts. 2. Acute myelogenous leukemia (AML), less than or equal to 25 percent marrow blasts. 3. Chronic myelogenous leukemia (CML). * Chronic phase, recurrent after or resistant to donor lymphocyte infusion (DLI) or resistant to available abl kinase inhibitors * Accelerated phase, less than 20 percent marrow blasts * Blastic phase, less than or equal to 25 percent marrow blasts 4. Myelodysplastic syndrome (MDS), less than 20 percent marrow blasts. 5. Non-Hodgkin's lymphoma (NHL), stage 4, less than or equal to 25 percent marrow blasts. 6. Hodgkin's lymphoma (HL) 7. There will be no restriction on the volume of extramedullary disease, with the exceptions of exclusions for central nervous system involvement or progression deemed unacceptably rapid. WT1 expression will be confirmed by at least one of the following criteria: * Greater than 15 percent of malignant cells react with anti-WT1 by immunohistochemistry. * Positive quantitative reverse transcription polymerase chain reaction (RT-PCR) of WT1 compared with a negative control. Human leukocyte antigen (HLA-A2) plus (heterozygous expression is acceptable). Prior stem cell transplantation (SCT): Prior HLA-matched (5-6/6 antigen or 8-10/10 allele) related or unrelated allogeneic SCT required. Must be at least 42 days post-transplant, have had recovery of transplant-associated toxicity to less than grade 2, and have post-transplant donor engraftment as defined by donor chimerism greater than 50 percent (peripheral blood), neutrophil recovery to an absolute neutrophil count (ANC) greater than 500/microl independent of myeloid growth factors, and platelet recovery to greater than 20,000/microL independent of transfusion. Disease status: Post-transplant residual or relapsed disease. Minimal residual disease (MRD) by polymerase chain reaction (PCR) or flow cytometry is acceptable in accordance with standard disease-specific diagnostic criteria. Availability of previous allogeneic donor to donate cells again. Prior therapy: Disease-specific therapy must be stopped at least 14 days prior to protocol Cycle 1 Day 1 (C1D1) and recovery of treatment-associated toxicity to greater than grade 2 is required prior to initiation of protocol therapy. Patients may have received prior DLI, but the last dose must be at least 28 days prior to C1D1 and there must be no active graft versus host disease (GVHD) greater than grade 1 acute or extensive chronic. Systemic immunosuppression must be stopped at least 28 days prior to protocol C1D1 and there must be no active GVHD greater than grade 1 acute or extensive chronic. There is no time restriction in regard to prior intrathecal chemotherapy provided there is complete recovery from any acute toxic effects of such. Patients receiving hydroxyurea are allowed. Performance status of 0, 1, 2, or 3. Renal function: Patients must have a serum creatinine less than or equal to 1.5 times the upper limit of normal based on age-specific normal range OR a creatinine clearance greater than or equal to 60 mL/min/1.73 m\^2. Hepatic function: Patients must have a total bilirubin less than or equal to 2.0 mg/dl and alanine aminotransferase (ALT) less than or equal to 5 times the upper limit of normal based on age- specific normal ranges. Ability to give informed consent. For patients less than 18 years of age, their legal guardian must give informed consent. Pediatric patients will be included in age appropriate discussion in order to obtain verbal assent. Recipients of unrelated donor transplants must sign a release of information form to authorize National Marrow Donor Program (NMDP) transfer of information to the National Institutes of Health (NIH). Subjects of childbearing or child-fathering potential must be willing to use a medically acceptable form of birth control, which includes abstinence, while they are being treated on this study. Inclusion Criteria: Donor Weight greater than or equal to 18 kg, and for unrelated donors only age greater than or equal to 18 years Previous HLA-matched related or unrelated allogeneic donor. Donors must be 5-6/6 antigen or 8-10/10 allele matched. HLA-A2 plus (heterozygous expression is acceptable). Adequate venous access for peripheral apheresis, or consent to use a temporary central venous catheter for apheresis. Donor selection will be in accordance with National Institutes of Health (NIH)/Clinical Center (CC) Department of Transfusion Medicine (DTM) criteria and, in the case of an unrelated donor, the National Marrow Donor Program (NMDP) standards. When a potentially eligible recipient of an unrelated donor product is identified, the recipient will complete an NMDP search transfer request to allow NIH NMDP staff to contact the NMDP Coordinating Center, who will, in turn, contact the donor's prior Donor Center. The NMDP Policy for Subsequent Donation Requests will be followed and the appropriate forms (Subsequent Donation Request form and Therapeutic T Cell Collection Prescription) will be submitted as required. Ability to give informed consent. For donors less than 18 years of age, their legal guardian must give informed consent. Pediatric donors must give verbal assent and be cleared by social work and a mental health specialist to participate. EXCLUSION CRITERIA: Exclusion Criteria: Patient Active graft versus host disease (GVHD) greater than grade 1 acute or extensive chronic. Breast feeding or pregnant females (due to risk to fetus or newborn). Central nervous system (CNS) malignancy by any of the following criteria: * Demonstration of malignant cells in the cerebrospinal fluid (CSF) in patients with leukemia or MDS as manifested by CSF white blood cell (WBC) greater than 5/microL and confirmation of CSF blasts. * Cranial neuropathies deemed secondary to the underlying malignancy. * CNS mass lesions deemed secondary to the underlying malignancy. * Neuroblastoma (NB): History of CNS involvement without current evidence of CNS malignancy is NOT an exclusion. Rapidly progressive malignancy and/or clinically significant systemic illness (e.g., severe unstable infections or organ dysfunction) that in the judgment of the PI would likely compromise the patient's ability to tolerate this therapy or interfere with the study procedures, including but not limited to a life expectancy of less than 3 months. High risk of inability to comply with protocol requirements as determined by principal investigator, social work, and primary team. Human immunodeficiency virus (HIV) infection or human T-lymphotrophic virus type 1 (HTLV-1) infection (due to associated immune suppression and decreased likelihood of developing an immune response to the vaccine and increased risk of severe infection). Active hepatitis B or C infection as defined by seropositive for hepatitis B surface antigen (HbSAg) or hepatitis C and elevated liver transaminases. Corticosteroids (dexamethasone equivalent up to 0.1 mg/kg/day) will be permitted. Topical agents and/or inhaled corticosteroids are permitted. Exclusion Criteria: Donor History of medical illness that in the estimation of the principal investigator (PI) or Department of Transfusion Medicine (DTM)/NMDP physician poses prohibitive risk to donation. Anemia (Hb less than 10 gm/dl) or thrombocytopenia (less than 100,000/microliter). Breast feeding or pregnant females (due to risk to fetus or newborn). High risk of inability to comply with protocol requirements as determined by the principal investigator and donor center team. Positive screening test for transfusion-transmissible infection in accordance with DTM or NMDP donation standards. Kaposi's sarcoma