Selumetinib and Cixutumumab in Treating Patients With Advanced Solid Malignancies

Inclusion Criteria: * Patients must have a histologically-confirmed metastatic or locally advanced solid tumor that has failed to respond to standard therapy, progressed despite standard therapy, or for which standard therapy does not exist * There is no limit on the number of prior treatment regimens * Patients must be off prior chemotherapy, radiation therapy, hormonal therapy, or biological therapy for at least 4 weeks; patients who were receiving mitomycin C, nitrosoureas, or carboplatin must be 6 weeks from the last administration of chemotherapy; patients with prostate cancer may continue to receive LHRH agonist (unless orchiectomy has been performed) * ECOG performance status 0-1 * Life expectancy of greater than 3 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,200/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 mg/dL * Albumin \>= 2.5 g/dL * Total bilirubin =\< 1.5 X institutional upper limits of normal in the absence of Gilbert's syndrome * AST(SGOT) and ALT(SGPT) =\< 2.5 X institutional upper limit of normal * Serum glucose =\< 120 mg/dL * Creatinine =\< 1.5 mg/dL OR creatinine clearance \>= 45 mL/min for patients with creatinine levels above institutional normal. * Patients must have recovered from toxicity related to prior therapy to at least grade 1 (defined by CTEP Active Version of the CTCAE); chronic stable grade 2 peripheral neuropathy secondary to neurotoxicity from prior therapies may be considered on a case by case basis by the Principal Investigator * As the effect of AZD6244 and IMC-A12 in combination on the developing human fetus is not known, women of child-bearing potential and men must agree to use adequate contraception (abstinence; hormonal or barrier method of birth control) for the study and at least 3 months after completion * Female patient of childbearing potential has a negative serum pregnancy test within 7 days of study enrollment * Ability to understand and the willingness to sign a written informed consent document * Measurable disease * Patient must be able to swallow pills * Patients must have LVEF \> 45% before starting therapy as measured by echocardiogram or MUGA * Patients should have a baseline ophthalmologic examination before starting therapy Exclusion Criteria: * Patient current evidence of active and uncontrolled infection, documented Child's class B-C cirrhosis, or active pancreatitis * Uncontrolled hypertension (BP \> 150/95 despite optimal therapy) * Left ventricular ejection fraction of =\< 45% or NYHA Class II-IV CHF * Prior or current cardiomyopathy * Atrial fibrillation with heart rate \> 100 bpm * Unstable ischemic heart disease (myocardial infarction within 6 months prior to starting treatment, or angina requiring use of nitrates more than once weekly) * Patients receiving any medications that are inhibitors or inducers of specific CYP450 enzyme(s) are ineligible * History of growth hormone deficiency or excess, or patient is concurrently using growth hormone (GH), or growth hormone inhibitors * Patient has a known hypersensitivity to the components of study drugs, its analogs, or drugs of similar chemical or biologic composition * Patient has prior exposure to IGF-1R or RAF/MEK inhibitors * The patient has poorly controlled diabetes mellitus, defined as a Hba1c \> 7% * Patients with active CNS metastases and/or carcinomatous meningitis are excluded; however, patients with CNS metastases who have completed a course of therapy would be eligible for the study provided they are clinically stable for 3 months prior to entry as defined as: * No evidence of new or enlarging CNS metastasis * No new signs or symptoms consistent with CNS metastasis * Off steroids or on a stable dose of steroids for at least four weeks * Patient with a primary central nervous system tumor * Patient has known psychiatric or substance abuse disorders that is uncontrolled and would interfere with cooperation with the requirements of the trial * Patient is pregnant or breastfeeding. * Patient is Human Immunodeficiency virus (HIV)-positive and on highly active antiretroviral therapy (HAART), as drug interactions between those agents and these experimental agents are wholly unknown; if this combination goes forward, this regimen will need to be tested in this group of patients in the future; patients with HIV who are well compensated and do not require HAART therapy are eligible for the study * Patient has active hepatitis B or C on treatment * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days of day 1 of therapy * Use of any other concurrent investigational agents or anticancer agents including hormonal therapy, except in the case of prostate cancer patients who are being treated with LHRH agonist at the time of trial entry * Patients should avoid excessive sun exposure and use adequate sunscreen protection if sun exposure is anticipated * History of any serious intraocular or retinal pathology as determined by the reference ophthalmologist, with the exception of controlled glaucoma or cataracts; in particular, patients with a history of retinal vein occlusion (RVC) or central serous retinopathy (CSR), or predisposing factors to RVO or CSR as assessed by ophthalmic exam (e.g. evidence of new optic disc cupping, new visual field defects, intraocular pressure \> 21 mmHg, uncontrolled glaucoma or ocular hypertension, uncontrolled systemic disease such as hypertension, diabetes mellitus, or history of hyperviscosity or hypercoagulability syndromes) must be excluded