MK2206 in Treating Younger Patients With Recurrent or Refractory Solid Tumors or Leukemia

Inclusion Criteria: * Patients must have a body surface area \> 0.5 m\^2 when enrolling on dose levels 0 or 1 of the every other day schedule; no body surface area (BSA) restrictions apply to patients enrolling on higher dose levels; no BSA restrictions apply to patients enrolling on any dose level of the weekly schedule. * Diagnosis: * Part A (both schedules): Patients must have a diagnosis of recurrent or refractory solid tumors, including central nervous system (CNS) tumors or lymphoma; patients must have had histologic verification of malignancy at original diagnosis or relapse except in patients with intrinsic brain stem tumors, optic pathway gliomas, or patients with pineal tumors and elevations of cerebrospinal fluid (CSF) or serum tumor markers including alpha-fetoprotein or beta-human chorionic gonadotropin (HCG) * Part B (both schedules): Patients must have a diagnosis of recurrent or refractory leukemia * Disease status: * Solid tumors: Patients must have either measurable or evaluable disease * Leukemia: Patients must have \>= 5% blasts in the bone marrow; active extramedullary disease (except for leptomeningeal disease) may also be present * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50% for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; note: neurologic deficits in patients with CNS tumors must have been relatively stable for a minimum of 1 week prior to study enrollment; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy * Myelosuppressive chemotherapy: * Solid tumors: Patients with solid tumors must not have received myelosuppressive chemotherapy within 3 weeks of enrollment onto this study (6 weeks if prior nitrosourea) * Leukemia: * Patients with leukemia who relapse while receiving standard maintenance chemotherapy will not be required to have a waiting period before enrollment onto this study * Patients who relapse while they are not receiving standard maintenance therapy, must have fully recovered from all acute toxic effects of prior therapy. At least 14 days must have elapsed since the completion of cytotoxic therapy, with the exception of hydroxyurea * Note: Cytoreduction with hydroxyurea can be initiated and continued for up to 24 hours prior to the start of MK-2206 * At least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 6 weeks since the completion of any type of immunotherapy, e.g. tumor vaccines * At least 3 half-lives of the antibody after the last dose of a monoclonal antibody * \>= 2 weeks for local palliative radiation therapy (XRT) (small port); \>= 24 weeks must have elapsed if prior total body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; \>= 6 weeks must have elapsed if other substantial bone marrow (BM) radiation * Stem cell infusion without TBI: No evidence of active graft vs. host disease and \>= 8 weeks must have elapsed since transplant or stem cell infusion * Bone marrow transplantation: \>= 3 months prior to study enrollment * For patients with solid tumors without known bone marrow involvement including patients who are status post stem cell transplantation: * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) * For patients with solid tumors with known bone marrow metastatic disease: * These patients are eligible for study provided they meet the blood count criteria and are not known to be refractory to red cell or platelet transfusions; note: these patients are not evaluable for hematologic toxicity * For patients with leukemia (Part B): * Blood counts are not required to be normal prior to enrollment on this trial; however, platelet count has to be \>= 20,000/mm\^3 (may receive platelet transfusions) * 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: 0.6 mg/dL * 2 to \< 6 years: 0.8 mg/dL * 6 to \< 10 years: 1 mg/dL * 10 to \< 13 years: 1.2 mg/dL * 13 to \< 16 years: 1.5 (male), 1.4 (female) * \>= 16 years: 1.7 (male), 1.4 (female) * Patients with solid tumors: * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Patients with leukemias: * Bilirubin (sum of conjugated + unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * SGPT (ALT) =\< 225 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Corrected QT interval (QTc) =\< 450 msec * Patients with seizure disorder may be enrolled if on non-enzyme inducing anticonvulsants and well controlled * Nervous system disorders (Common Terminology Criteria for Adverse Events \[CTCAE\] v4) resulting from prior therapy must be =\< grade 2 * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines * Slides or tissue blocks from either initial diagnosis or relapse must be available for central review; tissue blocks or slides must be sent; if tissue blocks or slides are unavailable, the study chair must be notified prior to study enrollment Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients receiving corticosteroids who have not been on a stable or decreasing dose of corticosteroid for the prior 7 days are not eligible * Patients who are currently receiving another investigational drug are not eligible * Patients who are currently receiving other anticancer agents are not eligible \[except leukemia patients receiving hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy\]; patients with leukemia may receive intrathecal therapy * Patients must not be receiving enzyme-inducing anticonvulsants * Patients receiving insulin or growth hormone therapy are not eligible * Patients on medications that may cause corrected QT (QTc) interval prolongation are not eligible * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post transplant are not eligible for this trial * Patients must be able to swallow whole tablets; nasogastric or G tube administration is not allowed * Patients who have an uncontrolled infection are not eligible * Patients with known type I or type II diabetes mellitus are not eligible * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible