• The patient must have histologically confirmed, gastric carcinoma, including gastroesophageal junction (GEJ) adenocarcinoma (patients with adenocarcinoma of the distal esophagus are eligible if the primary tumor involves the GEJ)

• The patient has metastatic disease or locally recurrent, unresectable disease

• The patient must have measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1

• The patient must have experienced disease progression during or within 4 months after the last dose of chemotherapy for metastatic disease, during or within 6 months after the last dose of adjuvant chemotherapy, or have been intolerant of previous chemotherapy

• The patient must have experienced disease progression or intolerance as outlined above after treatment with 1 or more prior chemotherapies

• All previous treatments are acceptable as long as they did not contain bevacizumab, ramucirumab or PARP inhibitors

• Elevation in tumor markers without radiographic evidence of disease progression is not satisfactory for progression on previous treatment

• The patient is \>= 18 years of age

• The patient has a life expectancy of \>= 16 weeks

• Eastern Cooperative Oncology Group (ECOG) performance status score of 0-1 (Karnofsky \>= 60%)

• Hemoglobin \>= 10 g/dL with no blood transfusions (packed red blood cells and platelet transfusions) in the past 28 days (within 28 days prior to administration of study treatment)

• White blood cells (WBC) \> 3 x 10\^9/L (within 28 days prior to administration of study treatment)

• Absolute neutrophil count (ANC) \>= 1.5 10\^9/L (within 28 days prior to administration of study treatment)

• Platelet count \>= 100 X 10\^9/L (within 28 days prior to administration of study treatment)

• No features suggestive of myelodysplastic syndrome (MDS)/acute myelogenous leukemia (AML) on peripheral blood smear or bone marrow biopsy, if clinically indicated (within 28 days prior to administration of study treatment)

• Total bilirubin =\< 1.5 x the institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment)

• Aspartate aminotransferases (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN unless liver metastases are present in which case they must be =\< 5 x ULN (within 28 days prior to administration of study treatment)

• Calculated serum creatinine clearance \>= 60 mL/min/1.73 m\^2 (within 28 days prior to administration of study treatment)

• Proteinuria with urinary protein =\< 1+ on dipstick or routine urinalysis, or a 24-hour urine collection for protein \< 1000 mg of protein in 24 hours (within 28 days prior to administration of study treatment)

• Coagulation parameters (international normalized ratio \[INR\], activated partial thromboplastin time \[aPTT\]) =\< 1.25 x institutional limits, except where a lupus anti-coagulant has been confirmed or the patient is on warfarin; patients on full dose anticoagulation must be on a stable dose for at least 14 days; if receiving warfarin, the patient must have an INR =\< 3.0 without any evidence of active bleeding within 14 days prior to first dose of study treatment or a pathologic condition that carries a high risk of bleeding (tumor involvement with major blood vessels or varices) (within 28 days prior to administration of study treatment)

• Postmenopausal or evidence of non-childbearing status for women of childbearing potential a negative urine or serum pregnancy test within 28 days of study treatment and confirmed prior to treatment on day 1; postmenopausal is defined as:

‣ Amenorrheic for 1 year or more following cessation of exogenous hormonal treatments

⁃ Luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50

⁃ Radiation-induced oophorectomy with last menses \> 1 year ago

⁃ Chemotherapy-induced menopause with \> 1 year interval since last menses

⁃ Surgical sterilization (bilateral oophorectomy or hysterectomy)

• The effects of olaparib and ramucirumab on the developing fetus are unknown; for this reason, women of child-bearing potential and men must agree to use adequate contraception including hormonal, barrier, or abstinence; contraception must be started prior to study enrollment; female patients of childbearing potential must have a negative serum pregnancy test within 7 days prior to treatment; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; both men and women treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of the study participation, and for 3 months after completion of olaparib and ramucirumab administration; male patients and their partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination, throughout the period of taking study treatment and for 3 months after last dose of study drug(s) to prevent pregnancy in a partner

• Ability to understand and the willingness to sign a written informed consent document

• The patient must be willing to undergo a biopsy prior to treatment, an on treatment biopsy at week 16 is optional if felt to be safe in the opinion of the investigator

• For inclusion into optional exploratory genetic and biomarker research, patients must fulfill the following criteria:

‣ Provision of informed consent for genetic research

⁃ Provision of informed consent for biomarker research

∙ If a patient declines to participate in the optional exploratory genetic research or the optional biomarker research, there will be no penalty or loss of benefit to the patient; the patient will not be excluded from other parts of the study

• Patients must be able to tolerate oral medications by mouth, and not have a gastrointestinal illness that would preclude absorption of olaparib

• Adequately controlled blood pressure (BP) \< 140 mmHg (systolic) and \< 90 mmHg (diastolic) taken in the clinic setting by a medical professional within 2 weeks prior to starting study; patients with hypertension may be managed with up to a maximum of 3 antihypertensive medications; a cardiologist or blood pressure specialist must evaluate patients who are on 3 antihypertensive medications within 4 weeks of enrollment

• Patients who have the following risk factors are considered to be at increased risk for cardiac toxicity and must have documented left ventricular ejection fraction (LVEF) by echocardiogram greater than institution's lower limit of normal (or 55% if threshold for normal not otherwise specified by institutional guidelines) obtained within 3 months

‣ Prior treatment with anthracyclines

⁃ Prior treatment with trastuzumab

⁃ A New York Heart Association (NYHA) classification of II controlled with treatment

⁃ Prior central thoracic radiation therapy (RT), including RT to the heart

⁃ History of myocardial infarction within 12 months (patients with history of myocardial infarction within 6 months are excluded)