• Patients must have histologically confirmed cancer for which standard-of-care curative measures are no longer effective or be intolerant to those agents. Patients in cohort 1 must have colorectal cancer. Patients in cohort 2 must have pancreatic cancer. Patients in cohort 3 may have any of the following cancers:

‣ Biliary

⁃ Gastroesophageal

⁃ Urothelial

⁃ Ovarian

⁃ Non-small cell lung (adenocarcinoma only)

• Patients must have measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 disease.

• Patients must have radiographic documentation of metastatic disease with imaging within =\< 6 weeks prior to registration.

• Patients must be age \>= 18 years.

• Patients must exhibit an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. Performance Status of 2 will be allowed with approval from principle investigator (PI) on a case-by case basis.

‣ Note: Performance status of 2 will be allowed with approval from PI on a case-by case basis. Documentation of PI approval in these cases will be stored with inclusion/exclusion signed checklist for patient and/or in patient's shadow chart.

• Patients must have exhausted all available molecularly targeted therapies (e.g., anti-PD-1/anti-PD-L1 agents where indicated).

• Absolute neutrophil count (ANC) \>= 1,500/mcL (within the last 14 days of screening)

• Hemoglobin (Hgb) \>= 9 g/dL (within the last 14 days of screening) (Transfusions permitted. Eligibility labs should be drawn \>= 7 days from transfusion).

• Platelets (PLT) \>= 100,000/mcL (within the last 14 days of screening) (Transfusions permitted. Eligibility labs should be drawn \>= 7 days from transfusion).

• INR (international normalized ratio) =\< 1.6 (within the last 14 days of screening) (unless receiving anticoagulation therapy) If receiving anticoagulant: INR =\< 3.0 and no active bleeding, (i.e., no bleeding within 14 days prior to first dose of study therapy).

• Total bilirubin =\<1.5 x Institutional upper limit of normal (ULN) (within the last 14 days of screening)

‣ Note: Patients with Gilbert's Syndrome are exempt. Patients with liver metastases with no significant bilirubin obstruction may have a total bilirubin level of =\< 2.0 mg/dL.

• Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT) =\< 2.5 x institutional ULN (within the last 14 days of screening)

‣ Note: If liver metastases are present, then =\< 5 x ULN is allowed.

• Alanine transaminase (ALT) serum glutamic-pyruvic transaminase (SGPT) =\< 2.5 x institutional ULN (within the last 14 days of screening)

‣ Note: If liver metastases are present, then =\< 5 x ULN is allowed.

• Serum albumin \> 3.0 g/dL (within the last 14 days of screening)

• Creatinine =\< 1.5 x ULN OR glomerular filtration rate (GFR) \>= 50 mL/min/1.73 m\^2 (within the last 14 days of screening)

‣ eGFR is estimated GFR calculated by the abbreviated Modification of Diet in Renal Disease (MDRD) equation

• The effects of combination treatment of CPI-613, 5-FU, gemcitabine, and HCQ on the developing human fetus are unknown. For this reason and because antineoplastic agents as well as other therapeutic agents used in this trial are known to be teratogenic, patients of child-bearing potential (POCBP) regardless of gender must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from time of informed consent, for the duration of study participation, and for 180 days following completion of therapy. Patients who can impregnate their partners regardless of gender must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) from time of informed consent, for the duration of study participation, and for 180 days following completion of therapy. Should a patient become pregnant or suspect they are pregnant while they or their partner is participating in this study, they should inform their treating physician immediately.

‣ Note: At the discretion of the investigator, acceptable methods of contraception may include total abstinence in cases where the lifestyle of the patient ensures compliance. (Periodic abstinence \[e.g., calendar, ovulation, symptothermal, postovulation methods\] and withdrawal are not acceptable methods of contraception.)

⁃ Note: A POCBP is any person with an egg-producing reproductive tract (regardless of sexual orientation, having undergone a tubal ligation, or remaining celibate by choice) who meets the following criteria:

• Has not undergone a hysterectomy or bilateral oophorectomy

∙ Has had menses at any time in the preceding 12 consecutive months (and therefore has not been naturally postmenopausal for \> 12 months)

• POCBP must have a negative pregnancy test prior to registration on study.

‣ Note: If negative pregnancy test result is \>7 days from first dose of study treatment it must be repeated at time of first dose of study treatment (with any of the four drugs used in this study).

• For patients with a known history of human immunodeficiency virus (HIV), infected patients on effective anti-retroviral therapy must have a viral load undetectable for 6 months prior to registration.

• For patients with a known history of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.

• Patients with a known history of hepatitis C virus (HCV) infection must have been treated and cured. Patients with HCV infection who are currently on treatment, must have an undetectable HCV viral load. Patients with known history or current symptoms of cardiac disease, or history of treatment with cardio toxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. Patients must be class 2B or better.

‣ Note: Patients with pacemakers where corrected QT interval (QTc) is not a reliable measure will require an evaluation by a cardiologist to exclude co-existing cardiac conditions which would prohibit safe participation in the study.

• Patients must have the ability to understand and the willingness to sign a written informed consent document for the duration of the entirety of the study.

• Patients must be reliable, willing to make themselves available for the duration of the entire study and willing to follow screening procedures.