Vatalanib and Pemetrexed Disodium in Treating Patients With Advanced Solid Tumors

Inclusion Criteria: * Willingness to return to Mayo Clinic Rochester for follow up * Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry, duration of study participation, and for at least 30 days after the last administration of study medication * ECOG performance status (PS) 0, 1, or 2 * Histologic proof of advanced solid tumor that has no known standard therapy that is potentially curative or definitely capable of extending life expectancy upon registration. * Mandatory translational research (MTD patients only): willingness to provide the biologic specimens as required by the protocol; willingness to undergo brachial artery ultrasound measurements * ANC \>= 1500/uL * Hgb \>= 9 g/dL * PLT \>= 100,000/uL * AST =\< 3 x ULN or AST =\< 5 x ULN if liver involvement * Calculated creatinine clearance \>= 45 ml/min * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Random urine protein:osmolality ratio =\< 0.40 OR total urinary protein =\< 500 mg and measured creatinine clearance (CrCl) \>= 45 mL/min from a 24-hour urine collection * Patients should have no contraindications to the intake of folic acid, vitamin B12 or dexamethasone * For patients with pleural/peritoneal/pericardial effusions: If patient is asymptomatic but the effusion volume is approximated to be \> 500 mL or produces measurable objective changes related to the effusion (e.g., echocardiographic ventricular compression, hypoxia on pulse oximetry, etc.), effusion should be drained * Able to permanently discontinue aspirin dose of \>=1.3 grams/day \>=10 days before through \>= 10 days after pemetrexed disodium treatment * Life expectancy \>= 12 weeks Exclusion Criteria: * Symptomatic, untreated, or uncontrolled CNS metastases or seizure disorder; patients with CNS metastases treated with whole brain radiation (WBRT) may be enrolled after completion of WBRT; patients may begin chemotherapy as early as the next day after WBRT * Any clinically significant infection * Active, bleeding diathesis or on any anticoagulant * HIV-positive patients receiving combination anti-retroviral therapy because of possible pharmacokinetic interactions with PTK/ZK * Chemotherapy =\< 3 weeks prior to registration * Radiation to \>= 30% of bone marrow * Immunotherapy =\< 2 weeks prior to registration * Chronic renal disease * Acute or chronic liver disease (e.g., hepatitis, cirrhosis) * Impairment of gastrointestinal (GI) function or GI disease since they may significantly alter the absorption of PTK/ZK (i.e., ulcerative disease, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, bowel obstruction, or inability to swallow tablets) * Greater than (\>) normal risk of bleeding or on any anticoagulant * Pregnant, nursing, or positive pregnancy test =\< 7 days prior to registration for women of childbearing potential * Symptomatic serosal effusion (\>= CTCAE v3.0 grade 2 dyspnea that is not amenable to drainage prior to registration) * Mitomycin C/nitrosoureas, bevacizumab =\< 6 weeks prior to registration * Biologic therapy =\< 2 weeks prior to registration * Other chemotherapy, immunotherapy, hormonal therapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-FDA approved indication and in the context of a research investigation) =\< 4 weeks prior to registration * Prolonged QTc (\> 450 msec for males and \> 470 msec for females) or known history of congenital or acquired prolonged QTc syndrome * Serious condition that, in the opinion of the investigator, would compromise the patient's ability to complete the study * Prior therapy with monoclonal antibody to VEGF, VEGF trap, small molecules with receptor tyrosine kinase activity against VEGFR, antisense oligonucleotide therapy against VEGF mRNA is allowed * Full field radiation therapy =\< 4 weeks prior to registration or limited field radiation therapy =\< 2 weeks prior to registration (the site of previous radiotherapy should have evidence of progressive disease if this is the only site of disease) * Men or women of childbearing potential who are unwilling to employ adequate contraception (a barrier method of birth control) (oral, implantable, or injectable contraceptives may be affected by cytochrome p450 interactions and are, therefore, not considered effective for this study) * a) Labile hypertension, or history of poor compliance with antihypertensive medication * d) Myocardial infarction =\< 6 months prior to registration * h) History of deep venous thrombosis or pulmonary embolism =\< 2 years prior to registration * Current use of the following drugs: amiodarone; anticoagulants (e.g., warfarin); anti-retroviral therapy (e.g., ritonavir); carbamazepine; chlorpromazine; cisapride; clarithromycin; clopidogrel; disopyramide; droperidol; erythromycin; fondaparinux; haloperidol; heparin; itraconazole; ketoconazole * Current use of the following drugs: methadone; oral contraceptives; phenobarbital; phenytoin; procainamide; products containing grapefruit juice; quinidine; rifabutin; rifampin; sotalol; sparfloxacin; St. John's Wort; thioridazine * i) Patients who require chronic treatment with PPI (e.g., omeprazole, lansoprazole, etc.) or H2 antagonist (e.g., ranitidine, famotidine, etc.) * Major surgery (i.e., laparotomy), open biopsy, or significant traumatic injury =\< 4 weeks prior to registration; minor surgery =\< 2 weeks prior to registration; insertion of a vascular access device is not considered major or minor surgery in this regard * b) Angina pectoris * c) History of congestive heart failure =\< 3 months prior to registration, unless ejection fraction \> 45% * f) Diabetes * g) Interstitial pneumonia or extensive and symptomatic interstitial fibrosis of the lung * Patients who have received prior treatment using pemetrexed disodium-containing regimens =\< 12 months prior to registration * Any of the following concurrent severe and/or uncontrolled medical conditions: * e) Cardiac arrhythmia