RATIONALE: Palifermin may help relieve or prevent oral mucositis caused by chemotherapy and radiation therapy in young patients undergoing stem cell transplant. PURPOSE: This randomized phase II trial is studying palifermin to see how well it works compared with a placebo in preventing oral mucositis caused by chemotherapy and/or radiation therapy in young patients undergoing stem cell transplant.

RATIONALE: Biological therapies, such as lenalidomide, may stimulate the immune system in different ways and stop cancer cells from growing. Drugs used in chemotherapy, such as fludarabine and cyclophosphamide, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving lenalidomide together with fludarabine and cyclophosphamide may kill more cancer cells. PURPOSE: This phase I/II trial is studying the side effects and best dose of lenalidomide when given together with fludarabine and cyclophosphamide and to see how well they work in treating patients with advanced chronic lymphocytic leukemia that did not respond to previous therapy.

RATIONALE: Methadone, morphine, or oxycodone may help relieve pain caused by cancer. It is not yet known whether methadone is more effective than morphine or oxycodone in treating pain in patients with cancer. PURPOSE: This randomized clinical trial is studying methadone to see how well it works compared with morphine or oxycodone in treating pain in patients with cancer.

RATIONALE: A donor peripheral stem cell transplant helps stop the growth of cancer cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Once the donated stem cells begin working, the patient's immune system may see the remaining cancer cells as not belonging in the patient's body and destroy them. Giving an infusion of donor T cells may helps stop the patient's immune system from rejecting the donor's stem cells. PURPOSE: This phase I/II trial is studying the side effects and best dose of donor T cells in treating patients with high-risk hematologic cancer who are undergoing donor peripheral blood stem cell transplant.

For relapsed and refractory leukemia patients induction chemotherapy prior to initiating a conditioning regimen will decrease residual leukemia (as measured by bone marrow leukemia blast percentage) at the time of HCT. This should lead to reduced relapse while still maintaining low transplant related mortality.

RATIONALE: Panobinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. PURPOSE: This phase II trial is studying the side effects of panobinostat and to see how well it works in treating patients with relapsed or refractory acute lymphoblastic leukemia or acute myeloid leukemia.

RATIONALE: Giving chemotherapy and total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from an unrelated donor, that do not exactly match the patient's blood, are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil before and after transplant may stop this from happening. PURPOSE: This phase II trial is studying how well umbilical cord blood transplant from an unrelated donor works in treating patients with hematologic cancer.

RATIONALE: Dasatinib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving dasatinib together with combination chemotherapy may kill more cancer cells. PURPOSE: This phase II trial is studying the side effects and how well giving dasatinib together with combination chemotherapy works in treating young patients with newly diagnosed acute lymphoblastic leukemia.

RATIONALE: Giving chemotherapy and total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer and abnormal cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from a related or unrelated donor, that do not exactly match the patient's blood, are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after transplant may stop this from happening. PURPOSE: This phase II trial is studying how well umbilical cord blood transplant given together with cyclophosphamide, fludarabine, and total-body irradiation works in treating patients with hematologic disease.

RATIONALE: Giving low doses of chemotherapy and total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer or abnormal cells. It may also stop the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil before and after transplant may stop this from happening. PURPOSE: This phase II trial is studying how well donor umbilical cord blood transplant works in treating patients with advanced hematological cancer or other disease.