Inclusion Criteria:

          -  Patients must have histologically confirmed AML or ALL, excluding acute promyelocytic
             leukemia (APL); for histological confirmation, a bone marrow biopsy and aspirate must
             be reviewed at Oregon Health & Science University (OHSU)

          -  Patients must have newly diagnosed AML or ALL without previous treatment; hydroxyurea
             will be allowed to control peripheral blast count as clinically indicated but would
             need to be stopped prior to initiation of tyrosine kinase inhibitor [TKI]); all-trans
             retinoic acid (ATRA) is permitted during the period prior to ruling out a diagnosis of
             APL; previous radiation treatment is allowable; patients must be deemed eligible for
             treatment with cytotoxic induction chemotherapy with cytarabine and idarubicin for AML
             or hyper-cyclophosphamide, dexamethasone, doxorubicin, vincristine sulfate (CVAD) for
             ALL; patients newly diagnosed with ALL must have received no prior treatment for their
             ALL with the exception of steroids (i.e. prednisone, dexamethasone); intrathecal
             methotrexate or cytarabine, allowed prior to and throughout the enrollment period for
             AML and ALL

          -  Subjects must be aged between >= 18 years and =< 64 for AML and > 40 and =< 64 for ALL

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2

          -  Total bilirubin < 2.0 x institutional upper limit of normal (ULN)

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x
             institutional ULN and thought to be due to hepatocellular dysfunction

          -  Potassium > lower limit of normal (LLN) or correctable with supplements prior to first
             dose of study medication

          -  Magnesium > LLN or correctable with supplements prior to first dose of study
             medication

          -  Total calcium (corrected for serum albumin) >= LLN or correctable with supplements
             prior to first dose of study medication

          -  Serum amylase and lipase =< 1.5 x institutional ULN

          -  International normalized ratio (INR) =< 2.0 or correctable to 2.0 with vitamin K
             therapy

          -  Corrected QT (QTc) =< 450 msec. for men or QTc =< 470 msec. for women

          -  Creatinine < 2.0 x ULN

          -  No clinically significant uncontrolled infections as determined by investigator

          -  Patients must be able to take oral medications

          -  Persons of reproductive potential must agree to an adequate method of contraception
             throughout treatment and for at least 4 weeks after study drug is stopped

               -  Women of childbearing potential must have a negative serum or urine pregnancy
                  test within 8 days prior to start of study drug administration

          -  Patients must be willing to accept blood product transfusions

          -  Ability to understand and the willingness to sign a written informed consent document
             and Health Insurance Portability and Accountability Act (HIPAA) documentation

          -  DRUG-SPECIFIC INCLUSION CRITERIA

          -  DASATINIB

               -  Women of childbearing potential (WOCBP) must have a negative serum or urine
                  pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human
                  chorionic gonadotropin [HCG]) within 24 hours prior to the start of study drug

               -  Women must not be breastfeeding

               -  WOCBP must agree to follow instructions for method(s) of contraception for the
                  duration of treatment with study drug, plus 30 days (duration of ovulatory cycle)
                  for a total of 30 days post-treatment completion

               -  Men who are sexually active with WOCBP must agree to follow instructions for
                  method(s) of contraception for the duration of treatment with study drug plus 90
                  days (duration of sperm turnover) for a total of 90 days post-treatment
                  completion

               -  Azoospermic males and WOCBP, who are not heterosexually active, are exempt from
                  contraceptive requirements; however, WOCBP must still undergo pregnancy testing

               -  Investigators shall counsel WOCBP and male subjects who are sexually active with
                  WOCBP on the importance of pregnancy prevention and the implications of
                  unexpected pregnancy; investigators shall advise WOCBP and male subjects who are
                  sexually active with WOCBP on the use of highly effective contraception; highly
                  effective methods of contraception have a failure rate of < 1% when used
                  consistently and correctly

               -  At a minimum, subjects must agree to the use of two methods of contraception,
                  with one method being highly effective and the other method being either highly
                  effective or less effective

        Exclusion Criteria:

          -  Newly diagnosed AML patients who are identified with FLT3-ITD or tyrosine kinase
             domain (TKD) point mutation in the codon for an aspartate (D835) or an isoleucine
             (I836) residue

          -  Patients with a diagnosis of Philadelphia chromosome (Ph)+ ALL are not eligible

          -  Subjects who are currently receiving any other investigational agents

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to study agent or other agents used in the study

          -  Drugs that affect the cytochrome P450 family 3, subfamily A, polypeptide 4 (CYP3A4)
             systems are allowed but should be used with caution depending on specific kinase
             inhibitor used

          -  All outside study medications and supplements will be reviewed and monitored by the
             inpatient pharmacy team; patients will be discouraged from taking herbals and
             additional supplements

          -  Patients should not be prescribed concomitant medications that may contribute to
             prolonged QTc without consultation with the chemotherapy pharmacist; additional ECGs
             should be done at the investigator?s discretion to ensure the subject?s safety; drugs
             that are generally accepted to increase the risk of Torsades de Pointes, include (but
             not limited to):

               -  Quinidine, procainamide, disopyramide

               -  Amiodarone, ibutilide, dofetilide, sotalol

               -  Erythromycin, clarithromycin

               -  Chlorpromazine, mesoridazine, thioridazine, pimozide

               -  Cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone,
                  halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine

          -  Left ventricular ejection fraction < 50%

          -  Uncontrolled intercurrent illness including but not limited to, symptomatic New York
             Heart Association (NYHA) class III congestive heart failure, uncontrolled angina
             pectoris, myocardial infarction or stroke within 6 months prior to enrollment, or
             psychiatric illness/social situations that would limit compliance with study
             requirements

          -  Patients with a known human immunodeficiency virus (HIV) diagnosis are excluded from
             the study

          -  History of hypersensitivity to any of the kinase inhibitors included in this study

          -  Pregnant or lactating women are excluded from the study

          -  Diagnosed congenital long QT syndrome

          -  Any history of significant bleeding disorder unrelated to cancer, including any
             congenital bleeding disorder or any acquired bleeding disorder within one year of
             start of study

          -  Any history of clinically significant ventricular arrhythmia (such as ventricular
             tachycardia, ventricular fibrillation or torsade de pointes)

          -  Patients must not have clinically significant malabsorption syndrome or history

          -  All patients must discontinue anti-platelet agents or anticoagulants 7 days prior to
             initiation of study drug

          -  All patients with unhealed wounds or fistulas should not be given vascular endothelial
             growth factor (VEGF) inhibiting TKIs

          -  DRUG-SPECIFIC EXCLUSION CRITERIA

          -  PONATINIB

               -  Patients with cytogenetically ?favorable risk' AML (core-binding factor
                  leukemias) will not be enrolled on the ponatinib arm; testing with cytogenetics
                  and fluorescence in situ hybridization (FISH) can establish this subtype within 7
                  days of the diagnostic bone marrow biopsy

               -  History of acute pancreatitis within 1 year of study or history of chronic
                  pancreatitis

               -  Uncontrolled hypertriglyceridemia (triglycerides > 450 mg/dL)

               -  Any history of myocardial infarction, stroke, or revascularization

                    -  Any history of venous thromboembolism including deep venous thrombosis or
                       pulmonary embolism with the exception of upper Extremity/Line associated
                       deep vein thrombosis (DVTs) which are adequately treated (line removed
                       and/or patient anti-coagulated)

               -  Uncontrolled hypertension (diastolic blood pressure > 90 mm Hg; systolic > 140 mm
                  Hg); patients with hypertension should be under treatment on study entry to
                  effect blood pressure control

          -  DASATINIB

               -  Any history of second or third degree heart block (may be eligible if the subject
                  currently has a pacemaker)

               -  Known pulmonary arterial hypertension

               -  Patients may not have clinically significant pleural or pericardial effusion per
                  provider discretion

          -  SORAFENIB

               -  Major surgery, open biopsy, or significant traumatic injury within 30 days

               -  Non-healing wound, ulcer, or bone fracture

               -  Thrombotic or embolic venous or arterial events, such as cerebrovascular
                  accident, including transient ischemic attacks, arterial thrombosis, deep vein
                  thrombosis and pulmonary embolism within the past 6 months

               -  Upper Extremity/Line associated DVTs which are adequately treated (line removed
                  and/or patient anticoagulated) are eligible

               -  Uncontrolled hypertension

               -  Active bleeding during screening

               -  Hypersensitivity to sorafenib

          -  Idelalisib

               -  Ongoing drug-induced liver injury, chronic active hepatitis C (hepatitis C virus
                  [HCV]), chronic active hepatitis B (hepatitis B virus [HBV]), alcoholic liver
                  disease, non-alcoholic steatohepatitis, primary biliary cirrhosis, extrahepatic
                  obstruction caused by cholelithiasis, cirrhosis of the liver, portal
                  hypertension, or history of autoimmune hepatitis

               -  Ongoing symptomatic pneumonitis

               -  Ongoing inflammatory bowel disease or autoimmune colitis

               -  Ongoing cytomegalovirus (CMV) infection, treatment, or prophylaxis within the
                  past 28 days prior to the screening test for active CMV

               -  History of serious allergic reaction including anaphylaxis and epidermal
                  necrolysis

          -  Ruxolitinib

               -  Chronic active hepatitis C (HCV)