Gemcitabine Hydrochloride, Cisplatin, and Nab-Paclitaxel in Treating Patients With Advanced or Metastatic Biliary Cancers

Inclusion Criteria: * Patient must have histologically or cytologically confirmed intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, or gallbladder cancer or may undergo a repeat biopsy for histologic confirmation if pre-existing biopsy is not sufficient for diagnosis * Metastatic or unresectable disease documented on diagnostic imaging studies * May not have received prior chemotherapy; if patient has received prior adjuvant therapy, must be \> 6 months from treatment * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Absolute neutrophil count (ANC) \>= 1,500 cells/mm\^3 * Platelets \>= 100,000/ul * Hemoglobin \> 9.0 g/dL * Total bilirubin =\< 1.5 mg/dL (in patients with known Gilbert's syndrome direct bilirubin =\< 1.5 x upper limit of normal \[ULN\] will be used as organ function criteria, instead of total bilirubin) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) = \< 5 x ULN * Creatinine =\< 1.5 gm/dL * Negative serum or urine pregnancy test in women with childbearing potential (WOCBP) defined as not post-menopausal for 12 months or no previous surgical sterilization, within one week prior to initiation of treatment; WOCBP must be using an adequate method of contraception to avoid pregnancy throughout the study and for up to 12 weeks after the last dose of study drug to minimize the risk of pregnancy * A male subject of fathering potential must use an adequate method of contraception to avoid conception throughout the study and for up to 12 weeks after the last dose of study drug to minimize the risk of pregnancy; if the partner is pregnant or breastfeeding, the subject must use a condom * Patients must sign an informed consent and authorization indicating that they are aware of the investigational nature of this study and the known risks involved Exclusion Criteria: * Peripheral neuropathy of grade 2 or greater by Common Terminology Criteria for Adverse Events (CTCAE) 4.0; in CTCAE version 4.0 grade 2 sensory neuropathy is defined as "moderate symptoms; limiting instrumental activities of daily living (ADLs)" * Concurrent severe and/or uncontrolled medical conditions which could compromise participation in the study such as unstable angina, myocardial infarction within 6 months, unstable symptomatic arrhythmia, uncontrolled diabetes, serious active or uncontrolled infection * Pregnancy (positive pregnancy test) or lactation * Known central nervous system (CNS) disease, except for treated brain metastasis; treated brain metastases are defined as having no evidence of progression or hemorrhage after treatment and no ongoing requirement for dexamethasone, as ascertained by clinical examination and brain imaging (magnetic resonance imaging \[MRI\] or computed tomography \[CT\]) during the screening period; anticonvulsants (stable dose) are allowed; treatment for brain metastases may include whole brain radiotherapy (WBRT), radiosurgery (RS; Gamma Knife, linear accelerator \[LINAC\], or equivalent) or a combination as deemed appropriate by the treating physician; patients with CNS metastases treated by neurosurgical resection or brain biopsy performed within 3 months prior to day 1 will be excluded