Inclusion Criteria:

          -  Age: 18 years of age or older (cohort 1 and cohort 2); 12 years of age or older
             (cohort 3)

          -  Histologically or cytologically confirmed sarcoma that fall into one of the following
             categories. Patients with low-grade tumors are eligible if there is definite evidence
             of metastasis or progression

               -  Angiosarcoma

               -  Dedifferentiated liposarcoma

               -  Osteosarcoma

          -  Must have received and have progressed, are refractory or intolerant to standard
             therapy appropriate for the specific sarcoma subtype, if there is a standard therapy
             for the subtype

          -  Subjects must have at least 1 lesion that is measurable by RECIST

               -  A previously irradiated lesion can be considered a target lesion if the lesion is
                  well defined, measurable per RECIST, and has clearly progressed since radiation

               -  Subjects undergoing fresh tumor biopsies must have additional non-target lesions
                  that can be biopsied at acceptable risk as judged by the investigator or if no
                  other lesions suitable for biopsy, then a RECIST target lesion used for biopsy
                  must be >= 2 cm in longest diameter

          -  Subjected must consent to provide archived tumor specimens for correlative biomarker
             studies. Tumor tissue must be identified and availability confirmed prior to
             initiation of study therapy. In the setting where archival material is unavailable or
             unsuitable for use, or there have been multiple intervening therapies subjects must
             consent and undergo fresh tumor biopsy. A tumor lesion planned for biopsy must not
             have a RECIST target lesion unless there are no other lesions suitable for biopsy and
             lesions used for biopsy is >= 2 cm in longest diameter

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (use Karnofsky
             for patients > 16 years and Lansky for patients =< 16)

          -  Absolute neutrophil count >= 1.5 x 10^9/L (1,500/mm^3) (without growth factor within
             28 days of first dose or transfusion within 14 days of first dose support)

          -  Platelet count >= 100 x 10^9/L (100,000/mm^3) (without growth factor within 28 days of
             first dose or transfusion within 14 days of first dose support)

          -  Hemoglobin >= 9.0 g/dL (without growth factor within 28 days of first dose or
             transfusion within 14 days of first dose support)

          -  Calculated creatinine clearance (CrCl) or 24-hour urine CrCl > 40 mL/min
             Cockcroft-Gault formula (using actual body weight) will be used to calculate CrCl

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN); for subjects with
             documented/suspected Gilbert's disease or liver metastases, bilirubin =< 3 x ULN

          -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 2.5 x ULN; for
             subjects with hepatic metastases, ALT and AST =< 5 x ULN

          -  Female patients of childbearing potential who are not abstinent and intend to be
             sexually active with a non-sterilized male partner must use at least 1 highly
             effective method of contraception (defined below) from the time of screening
             throughout the total duration of the drug treatment and the drug washout period (90
             days after the last dose of durvalumab monotherapy). Non-sterilized male partners of a
             female patient of childbearing potential must use male condom plus spermicide
             throughout this period. Cessation of birth control after this point should be
             discussed with a responsible physician. Periodic abstinence, the rhythm method, and
             the withdrawal method are not acceptable methods of birth control. Female patients
             should also refrain from breastfeeding throughout this period.

          -  Non-sterilized male patients who are not abstinent and intend to be sexually active
             with a female partner of childbearing potential must use a male condom plus spermicide
             from the time of screening throughout the total duration of the drug treatment and
             drug washout period (90 days after the last dose of durvalumab monotherapy). However,
             periodic abstinence, the rhythm method, and the withdrawal method are not acceptable
             methods of contraception. Male patients should refrain from sperm donation throughout
             this period

          -  Female partners (of childbearing potential) of male patients must also use a highly
             effective method of contraception throughout this period as defined below. Notes:
             Females of childbearing potential are defined as those who are not surgically sterile
             (i.e., bilateral salpingectomy, bilateral oophorectomy, or complete hysterectomy) or
             post-menopausal. Women will be considered post-menopausal if they have been
             amenorrheic for 12 months without an alternative medical cause. The following
             age-specific requirements apply:

               -  Women < 50 years of age would be considered post-menopausal if they have
                  amenorrheic for 12 months or more following cessation of exogenous hormonal
                  treatments and if they have luteinizing hormone and follicle-stimulating hormone
                  levels in the post-menopausal range for the institution.

               -  Women >= 50 years of age would be considered post-menopausal if they have
                  amenorrheic for 12 months or more following cessation of all exogenous hormonal
                  treatment, had radiation-induced menopause with last menses > 1 year ago, had
                  chemotherapy-induced menopause with last menses > 1 year ago.

        Highly effective methods of contraception, defined as one that results in a low failure
        rate (i.e., less than 1% per year) when used consistently and correctly are described
        below. Note that some contraception methods are not considered highly effective (e.g. male
        or female condom with or without spermicide; female cap, diaphragm, or sponge with or
        without spermicide; non-copper containing intrauterine device; progesterone-only oral
        hormonal contraceptive pills where inhibition of ovulation is not the primary mode of
        action [excluding Cerazette/desogestrel which is considered highly effective]; and
        triphasic combined oral contraceptive pills.

          -  Copper T intrauterine device

          -  Levonorgestrel-releasing intrauterine system: e.g., Mirena

          -  Implants: Etonogestrel-releasing implants: e.g. Implanon or Norplant

          -  Injection: Medroxyprogesterone injection: e.g., Depo-Provera

          -  Combined pill: Normal and low dose combined oral contraceptive pill

          -  Patch: Norelgestromin/ethinylestradiol-releasing transdermal system: e.g., Ortho Evra

          -  Minipill: Progesterone based oral contraceptive pill using desogestrel: Cerazette is
             currently the only highly effective progesterone-based

               -  Life expectancy of at least 6 months

               -  Ability to understand the purposes and risk of the study and has signed a written
                  consent form approved by the investigator's Institutional Review Board
                  (IRB)/Ethics Committee

               -  Weight >= 35 kg

        Exclusion Criteria:

          -  Prior therapy with anti-PD1, anti-PD-L1 (including durvalumab) or anti-CD73

          -  Active or prior documented autoimmune disease (including inflammatory bowel disease,
             celiac disease, Wegener syndrome) within the past 2 years. Subjects with childhood
             atopy or asthma, vitiligo, alopecia, Hashimoto syndrome, Grave's disease, or psoriasis
             not requiring systemic treatment (within the past 2 years) are not excluded

          -  Untreated central nervous system metastatic disease, leptomeningeal disease, or cord
             compression. Subjects previously treated central nervous system metastases that are
             radiographically and neurologically stable for at least 28 days and do not require
             corticosteroids (or any dose) for symptomatic management for at least 14 days prior to
             first dose of durvalumab and oleclumab are permitted to enroll

          -  Concurrent enrollment in another clinical study, unless it is an observational
             (non-interventional) clinical study or the follow-up period of an interventional study

          -  Receipt of any conventional or investigational anticancer therapy within 21 days prior
             to the first dose of study drug

          -  Any concurrent chemotherapy, immunotherapy, or biologic or hormonal therapy for cancer
             treatment. Concurrent use of hormones for non-cancer-related conditions (e.g., insulin
             for diabetes and hormone replacement therapy) is acceptable. In addition, local
             treatment (e.g., by local surgery or radiotherapy) of isolated lesions for palliative
             intent is acceptable beyond the first cycle with prior consultation and in agreement
             with the principal investigator (PI)

          -  Unresolved toxicities from prior anticancer therapy, defined as having not resolved to
             National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE)
             version (v)5.0 grade 0 or 1 with the exception of alopecia and laboratory values
             listed per the inclusion criteria. Subjects with irreversible toxicity that is not
             reasonably expected to be exacerbated by any of the investigational products may be
             included (e.g., hearing loss) after consultation with the medical monitor

          -  Current or prior use of immunosuppressive medication within 14 days prior to the first
             of durvalumab or oleclumab. The following are exceptions to this criterion:

               -  Intranasal, inhaled, topical steroids, or local steroid injections (e.g.,
                  intra-articular injection)

               -  Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of
                  prednisone or equivalent

               -  Steroids as premedication for hypersensitivity reactions (e.g., computed
                  tomography [CT] scan premedication)

          -  History of primary immunodeficiency, solid organ transplantation, or previous clinical
             diagnosis of tuberculosis

          -  True positive test results for human immunodeficiency virus (HIV) or hepatitis B or
             hepatitis C

          -  Receipt of live, attenuated vaccine within 30 days prior to the first dose of
             investigational products (NOTE: Subjects, if enrolled, should not receive live vaccine
             during the study and 180 days after the last dose of investigational products)

          -  Major surgery (as defined by the investigator) within 4 weeks or thoracotomy for
             pulmonary metastases within 2 weeks prior to first dose of treatment or if still
             recovering from prior surgery. Local surgery of isolated lesions for palliative intent
             is acceptable

          -  Other invasive malignancy, within 2 years except for noninvasive malignancies such as
             cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma
             in situ of the breast that has/have been surgically cured

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable
             angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, or
             psychiatric illness/social situations that would limit compliance with study
             requirement, substantially increase risk of incurring adverse events (AEs) from
             durvalumab or oleclumab, or compromise the ability of the subject to give written
             informed consent

          -  Any condition that, in the opinion of the investigator or sponsor, would interfere
             with evaluation of the investigational product or interpretation of subject safety or
             study results

          -  Patients with a history of pneumonitis (active within past 6 months) or interstitial
             lung disease

          -  Subjects with a history of venous thrombosis within the past 3 months

          -  Subjects prior history of myocardial infarction, transient ischemic attack, or stroke
             in the last 3 months