Inclusion Criteria: -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Relapsed or refractory ALL after multi-agent chemotherapy (>= 5% marrow lymphoblasts, assessed by morphology and flow cytometry; flow cytometry will be used to confirm immunophenotype and percentage of blasts will be assessed by morphology) -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Eastern Cooperative Oncology Group (ECOG) performance status 0-2 -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Adequate liver function with aspartate aminotransferase (AST)/alanine aminotransferase (ALT) less than 3 X upper limit of normal and total bilirubin less than 2 mg/dL within 7 days prior to first dose of study agent -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Circulating white blood cell (WBC) count must not be above 20 x10^9/L within 7 days prior to first dose of study agent -Patients with WBC count above 20 x 10^9/L may be eligible if they start steroids or hydroxyurea per institutional guidelines, but they must discontinue before day 1 of study drug -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Creatinine clearance of at least 50 mL/min within 7 days prior to first dose of study agent -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Women must not be pregnant or breast-feeding -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy; a female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Women of childbearing potential and sexually active males must use an accepted and highly effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study and for 30 days after the last dose of venetoclax; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she (or the participating partner) should inform the treating physician immediately -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, or any surgically- or radiation-cured malignancy continuously disease free for >= 5 years so as not to interfere with interpretation of radiographic response -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): No evidence of isolated extramedullary relapse (i.e., testicular or central nervous system [CNS]) -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patient must not have Burkitt?s lymphoma/leukemia based on the World Health Organization (WHO) criteria -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local treatment for active disease within the prior 28 days; previously treated CNS disease with documented cleared CSF will be allowed -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patient will not be enrolled if they received prior chemotherapy within 2 weeks before enrollment with the following exceptions: to reduce the circulating lymphoblast count or palliation (i.e., steroids or hydroxyurea) or for ALL maintenance (mercaptopurine, methotrexate, vincristine, thioguanine, and/or tyrosine kinase inhibitors) -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active graft versus host disease (GVHD) prior to enrollment if previous HSCT -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patient cannot have poorly controlled human immunodeficiency virus (HIV), or CD4 < 400; HIV positive patients are allowed on this study if they have a CD4 count >= 400, and are on a stable antiviral regimen -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients with New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia may not be enrolled -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients with serious medical or psychiatric illness that in the opinion of the primary investigator is likely to interfere with study participation may not be enrolled -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients must not be participating in any other clinical trial or taking any other experimental medications within 21 days prior to registration -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients should not have received the following within 7 days prior to the first dose of study drug: -Steroid therapy for anti-neoplastic intent; -Strong and moderate CYP3A inhibitors; -Strong and moderate CYP3A inducers -ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patients must not have grade 3 or higher peripheral neuropathy -ELIGIBILITY CRITERIA - PHASE II (ARM D): Relapsed or refractory ALL after multi-agent chemotherapy (>= 5% marrow lymphoblasts, assessed by morphology and flow cytometry; flow cytometry will be used to confirm immunophenotype and percentage of blasts will be assessed by morphology) -ELIGIBILITY CRITERIA - PHASE II (ARM D): ECOG performance status 0-2 -ELIGIBILITY CRITERIA - PHASE II (ARM D): Adequate liver function with AST/ALT less than 3 X upper limit of normal and total bilirubin less than 2 mg/dL within 7 days prior to first dose of study agent -ELIGIBILITY CRITERIA - PHASE II (ARM D): Circulating WBC count must not be above 20 x10^9/L within 7 days prior to first dose of study agent -Patients with WBC count above 20 x10^9/L may be eligible if they start steroids or hydroxyurea per institutional guidelines, but they must discontinue before day 1 of study drug -ELIGIBILITY CRITERIA - PHASE II (ARM D): Creatinine clearance of at least 50 mL/min within 7 days prior to first dose of study agent -ELIGIBILITY CRITERIA - PHASE II (ARM D): Women must not be pregnant or breast-feeding -ELIGIBILITY CRITERIA - PHASE II (ARM D): All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy; a female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) -ELIGIBILITY CRITERIA - PHASE II (ARM D): Women of childbearing potential and sexually active males must use an accepted and highly effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study and for 30 days after the last dose of venetoclax; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she (or the participating partner) should inform the treating physician immediately -ELIGIBILITY CRITERIA - PHASE II (ARM D): No evidence of prior malignancy except adequately treated non-melanoma skin cancer, in situ cervical carcinoma, or any surgically- or radiation-cured malignancy continuously disease free for >= 5 years so as not to interfere with interpretation of radiographic response -ELIGIBILITY CRITERIA - PHASE II (ARM D): No evidence of isolated extramedullary relapse (i.e., testicular or CNS) -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient must not have Burkitt?s lymphoma/leukemia based on the WHO criteria -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients must not have active central nervous system (CNS) leukemia, as defined by unequivocal morphologic evidence of lymphoblasts in the cerebrospinal fluid (CSF), use of CNS-directed local treatment for active disease within the prior 28 days; previously treated CNS disease with documented cleared CSF will be allowed -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient will not be enrolled if they received prior chemotherapy within 2 weeks before enrollment with the following exceptions: to reduce the circulating lymphoblast count or palliation (i.e., steroids or hydroxyurea), for ALL maintenance (mercaptopurine, methotrexate, vincristine, thioguanine, and/or tyrosine kinase inhibitors) -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active GVHD prior to enrollment if previous HSCT -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patient cannot have poorly controlled HIV, or CD4 < 400; HIV positive patients are allowed on this study if they have a CD4 count >= 400, and are on a stable antiviral regimen -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients with NYHA class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia may not be enrolled -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients with serious medical or psychiatric illness that in the opinion of the primary investigator is likely to interfere with study participation may not be enrolled -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients must not be participating in any other clinical trial or taking any other experimental medications within 21 days prior to registration -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients should not have received the following within 7 days prior to the first dose of study drug: -Steroid therapy for anti-neoplastic intent; -Strong and moderate CYP3A inhibitors; -Strong and moderate CYP3A inducers -ELIGIBILITY CRITERIA - PHASE II (ARM D): Patients must not have grade 3 or higher peripheral neuropathy