Inclusion Criteria:

• Histologically or cytologically confirmed diagnosis of small cell neuroendocrine carcinoma with no prior systemic treatment
• Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) with conventional techniques or as >= 10 mm (>= 1 cm) with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)
• White blood cell count (WBC) >= 3 x 10^9/L
• No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear
• Absolute neutrophil count >= 1,500/mcL
• Platelets >= 100,000/mcL
• Hemoglobin >= 10 g/dL
• Total bilirubin =< 1.5 x institutional upper limit of normal (ULN)
• Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =< 2.5 x institutional ULN, unless liver metastases are present and then =< 5 x institutional ULN is acceptable
• Creatinine =< 1.5 x institutional ULN
• Creatinine clearance >= 60 mL/min/1.73 m^2 for patients with creatinine levels above 1.5 x institutional ULN
• Proteinuria =< 2+ proteinuria on two consecutive urinalysis/dipstick tests taken no less than 1 week apart; patients with 2+ proteinuria on dipstick must also have a 24 hour urine collection demonstrating =< 500 mg over 24 hours
• Urine protein: creatinine ratio (UPC) of =< 1; UPC is the preferred test
• Ability to swallow and retain oral medication
• Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of olaparib and cediranib administration
• Ability to understand and the willingness to sign a written informed consent document
• Participants must have archival tumor tissue available for analysis or be able to undergo a baseline fresh tumor tissue biopsy

Exclusion Criteria:

• Patients who have had major surgery or trauma within 28 days prior to entering the study
• Patients who have had radiotherapy within 14 days prior to entering the study
• Patients with a non-healing wound, fracture, or ulcer
• Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities > Common Terminology Criteria for Adverse Events [CTCAE] grade 1 or baseline, with the exception of alopecia)
• Patients who are receiving any other investigational agents
• Patients with symptomatic central nervous system (CNS) metastases or leptomeningeal carcinomatosis should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; exceptions include patients with previously-treated CNS metastases who are asymptomatic and have no requirement for steroids or anti-seizure medication for at least one week prior to study entry; screening with CNS imaging studies (CT scan or MRI) is required
• History of allergic reactions attributed to compounds of similar chemical or biologic composition to olaparib, cediranib, carboplatin, cisplatin, or etoposide
• Patients with a history of myelodysplastic syndrome (MDS)
• Patients with a history of acute myeloid leukemia (AML), or patients with a history of any other primary malignancy within 3 years prior to initiation of treatment on this study; exceptions include: patients with a history of malignancies (other than AML) that were treated curatively and have not recurred within 3 years prior to study entry; resected basal and squamous cell carcinomas of the skin; and completely resected carcinoma in situ of any type
• Patients with clinically significant gastrointestinal abnormalities including, but not limited to: malabsorption syndrome, major resection of the stomach or small bowel that could affect the absorption of the study drugs, inflammatory bowel disease, ulcerative colitis, or other gastrointestinal conditions with increased risk of perforation as judged by the treating investigator
• Patients with a history of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 28 days prior to beginning study treatment
• Patients with poorly controlled hypertension (defined as systolic blood pressure [SBP] of >= 140 mmHg or diastolic blood pressure [DBP] of >= 90 mmHg); Note: Initiation or adjustment of antihypertensive medication(s) is permitted prior to study entry; blood pressure must be re-assessed on two occasions that are separated by a minimum of 1 hour; the mean SBP/DBP values from each blood pressure assessment must be < 140/90 mmHg in order for a subject to be eligible for the study; the blood pressure must be < 140/90 mmHg on the day of first dose of study drug
• Patients with a history of cerebrovascular accident including transient ischemic attack (TIA), pulmonary embolism or insufficiently treated deep venous thrombosis (DVT) within the past 3 months; Note: Participants with recent DVT who have been treated with therapeutic anti-coagulants for at least 6 weeks are eligible, with the exception of participants being treated with warfarin, which is prohibited on this study; other oral anti-coagulants may be allowed after discussion with overall principle investigator (PI), but short half-life low molecular weight heparins are strongly preferred
• Patients with evidence of active bleeding diathesis
• Patients with hemoptysis in excess of 2.5 mL within 6 weeks prior to the first dose of study medication
• Patients receiving any medications or substances that are potent inhibitors or inducers of CYP3A4 are ineligible
• Patients requiring concomitant therapy with phenytoin, phenobarbital, carbamazepine, or valproic acid
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
• Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with olaparib or cediranib
• Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible