Combination Chemotherapy With or Without Vismodegib in Treating Patients With Advanced Stomach Cancer or Gastroesophageal Junction Cancer

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed gastric or gastroesophageal junction (GEJ) adenocarcinoma not amenable to surgical resection
* 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) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral computed tomography (CT) scan
* No prior chemotherapy for advanced disease; patients may have receive adjuvant chemotherapy or chemoradiation if \> 6 months has elapsed since completion of treatment
* Life expectancy of greater than 3 months
* Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 70%)
* Absolute neutrophil count \>= 1,500/mcL
* Platelets \>= 100,000/mcL
* Total bilirubin =\< 1.5 times 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 upper limit of normal (=\< 5.0 X institutional upper limit of normal with presence of liver metastases)
* Creatinine =\< 1.5 X institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal
* Baseline imaging studies performed =\< 28 days of study registration; the treating investigator will determine the appropriate imaging studies, which may include CT scan, magnetic resonance imaging (MRI), and/or fludeoxyglucose F 18 (FDG)-positron emission tomography (PET)/CT
* Must be willing to provide blood and tissue samples for research purposes; patient has the right to later withdraw consent for research studies and/or tissue specimens
* Patients must agree to placement of a central venous catheter for chemotherapy administration
* Patients must be able to swallow whole capsules
* Patients taking medications with narrow therapeutic indices that are metabolized by cytochrome P450 (CYP450), including warfarin sodium (Coumadin), must be on a stable, therapeutic dose and have close monitoring of their levels
* Women of child-bearing potential and men must use two forms of contraception (i.e., barrier contraception and one other method of contraception) at least 4 weeks prior to study entry, for the duration of study participation, and for at least 12 months post-treatment; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately
* Pregnancy testing: women of childbearing potential are required to have a negative serum pregnancy test (with a sensitivity of at least 25 mIU/mL) within 10-14 days and within 24 hours prior to the first dose of GDC-0449/placebo (serum or urine); a pregnancy test (serum or urine) will be administered every 4 weeks if their menstrual cycles are regular or every 2 weeks if their cycles are irregular while on study within the 24-hour period prior to the administration of GDC-0449/placebo; a positive urine test must be confirmed by a serum pregnancy test; prior to dispensing GDC-0449/placebo, the investigator must confirm and document the patient's use of two contraceptive methods, dates of negative pregnancy test, and confirm the patient's understanding of the teratogenic potential of GDC-0449/placebo
* Female subjects of childbearing potential are defined as follows:

  * Patients with regular menses
  * Patients, after menarche with amenorrhea, irregular cycles, or using a contraceptive method that precludes withdrawal bleeding
  * Women who have had tubal ligation
* Female subjects may be considered to NOT be of childbearing potential for the following reasons:

  * The patient has undergone hysterectomy and/or bilateral oophorectomy.
  * The patient is post-menopausal defined by amenorrhea for at least 1 year in a woman \> 45 years old
* Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

* Patients who have had chemotherapy or radiotherapy within 6 months prior to entering the study
* Patients may not be receiving any other investigational agents
* Patients with known brain metastases should be excluded from this clinical trial
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to GDC-0449, 5-fluorouracil or oxaliplatin
* GDC-0449 inhibits cytochrome P450, family 2, subfamily C, polypeptide 8 (CYP2C8), cytochrome P450, family 2, subfamily C, polypeptide 9 (CYP2C9), and cytochrome P450, family 2, subfamily C, polypeptide 19 (CYP2C19) drug metabolism enzymes in vitro at concentrations that may be clinically relevant; therefore, caution should be exercised when dosing GDC-0449 concurrently with medications that are substrates of CYP2C8, CYP2C9, and CYP2C19 and have narrow therapeutic windows
* Patients with malabsorption syndrome or other condition that would interfere with intestinal absorption
* Patients unable to swallow whole capsules
* Patients with clinically active liver disease, including viral or other hepatitis or cirrhosis are ineligible
* Patients with uncontrolled hypocalcemia, hypomagnesemia, hyponatremia or hypokalemia defined as less than the lower limit of normal for the institution, despite adequate electrolyte supplementation are excluded from this study
* Pre-existing \> grade 1 peripheral sensory neuropathy
* Previous or concurrent malignancy; exceptions: treated basal cell or squamous cell skin cancer, in situ cervical cancer, or lobular carcinoma in situ in one breast; or other cancer which the patient has been disease-free ≥5 years
* 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 GDC-0449
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible