Modified Immune Cells (Autologous Dendritic Cells) and a Vaccine (Prevnar) Combined With Immune Checkpoint Inhibition After High-Dose External Beam Radiation Therapy in Treating Patients With Unresectable Liver Cancer

Inclusion Criteria: * Age \>= 18 years * Pilot study (group 1): Histologic confirmation of intrahepatic CCA (Closed as of amendment 3) * Phase II study (group 2): Histologic and/or radiologic confirmation of hepatocellular carcinoma (HCC) * Phase II study (group 3): Histologic confirmation of intrahepatic cholangiocarcinoma (iCCA) * The following tumor characteristics must be met * Unresectable disease: HCC (group 2) or intrahepatic CCA (group 3) * Measurable or evaluable disease * All lesions should be treatable by EBRT while meeting normal tissue constraints * Tumor lesions should be accessible using an ultrasound (US)-guided approach for intratumoral DC injection * No evidence of extrahepatic tumor (excluding tumor thrombus) by computed tomography (CT) or magnetic resonance imaging (MRI) scan * NOTE: Patients who are not candidates for surgical treatment or for ablation with curative intent are allowed * Good candidate for standard of care high-dose conformal EBRT in the view of the investigator * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1 * GROUP 2 HCC ONLY: Absolute neutrophil count (ANC) \>= 1000/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Absolute lymphocyte count (ALC) \>= 500/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Absolute monocyte count (AMC) \>= 300/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Platelet count \>= 50,000/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Hemoglobin \>= 9.0 g/dL (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Total bilirubin \< 1.5 mg/dL (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 5 x upper limit of normal (ULN) (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Creatinine =\< 2 mg/dL (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) =\< 1.5 x ULN (obtained =\< 15 days prior to registration) * GROUP 2 HCC ONLY: Absence of proteinuria at screening as demonstrated by one of the following: * Urine protein/creatinine (UPC) ratio \< 1.0 at screening OR * Urine dipstick for proteinuria \< 2+ (patients discovered to have \>= 2+ proteinuria on dipstick urinalysis at baseline should undergo a 24-hour urine collection and must demonstrate =\<1g of protein in 24 hours to be eligible) * GROUP 3 iCCA ONLY: Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Absolute lymphocyte count ≥ 500/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Absolute monocyte count ≥ 300/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Platelet count ≥ 100,000/mm\^3 (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Hemoglobin ≥ 9.0 g/dL (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Total bilirubin \< 1.5 x ULN (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) and alkaline phosphatase (ALP) ≤ 2.5 x ULN (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Creatinine ≤ 2 mg/dL (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: Serum albumin ≥ 25 g/L (2.5 g/dL) (obtained =\< 15 days prior to registration) * GROUP 3 iCCA ONLY: PT/INR/aPTT ≤ 1.5 x ULN (obtained =\< 15 days prior to registration) * NOTE: If patient is receiving therapeutic anticoagulation, patient must be on a stable anticoagulant regimen * GROUP 3 iCCA ONLY: Calcium ≤ 12 mg/dl or corrected serum calcium ≤ ULN (obtained =\< 15 days prior to registration) * Negative pregnancy test done =\< 8 days prior to registration, for persons of childbearing potential only * GROUP 3 ONLY: Negative hepatitis B surface antigen (HBsAg) test at screening * GROUP 3 ONLY: Negative hepatitis C virus antibody (HCV Ab) test at screening, or positive HCV antibody test followed by a negative HCV ribonucleic acid (RNA) test at screening. (NOTE: HCV RNA test will be performed only for patients who have a positive HCV antibody test.) * Ability to provide written consent * Willingness to return to enrolling institution for follow-up (during the active monitoring phase of the study) * Willingness to provide blood and tissue samples for correlative research purposes Exclusion Criteria: * Any of the following because this study involves an investigational agent, the genotoxic, mutagenic and teratogenic effects of which on the developing fetus and newborn are unknown: * Pregnant persons * Nursing persons * Persons of childbearing potential who are unwilling to employ highly effective contraception during heterosexual intercourse while on this study and for 5 months after the last dose of study medication * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients and patients known to be HIV positive. * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial if they are stable on anti-retroviral therapy, have a CD4+ T cell count ≥ 200/uL, and have an undetectable viral load * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection requiring systemic treatment or that could impact patient safety * Severe infection ≤ 4 weeks prior to registration, including, but not limited to, hospitalization for complications of infection, bacteremia, or severe pneumonia * Significant cardiovascular disease (New York Heart Association \[NYHA\] class II), symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia * Or, psychiatric illness/social situations (e.g., substance abuse) that would limit compliance with study requirements * Receiving any other investigational agent that would be considered a treatment for the primary neoplasm * Other active malignancy =\< 1 year prior to registration that is considered by the investigator to interfere with the current treatment or measurement of outcomes * Major surgery =\< 4 weeks prior to enrollment (other than diagnostic surgery or surgical spacer placement in preparation for radiation treatment), or anticipation of need for a major surgical procedure during the study * History of hypersensitivity or anaphylactoid reactions to pneumococcal vaccine or any component of the formulation, including diphtheria toxoid * Active or history of autoimmune disease or immune deficiency, including but not limited to,myasthenia gravis, myositis, autoimmune hepatitis, Crohn's disease, inflammatory bowel disease, antiphospholipid antibody syndrome, rheumatoid arthritis, Sjogren syndrome, systemic lupus erythematosus, Guillain-Barre syndrome, multiple sclerosis, Wegener granulomatosis, or similar conditions * NOTE: Exceptions are allowed for: * Patients with hypothyroidism on thyroid replacement therapy * Patients with type 1 diabetes mellitus on insulin regimen * Patients with eczema, psoriasis lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of the following conditions are met: * Rash must cover \< 10% of body surface area * Disease is well controlled at baseline and requires only low-potency topical corticosteroids * There has been no occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet A radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids ≤ 12 months prior to registration * Requires anticoagulant treatment (INR \> 1.5 x ULN) or use of anti-platelet agents that cannot be discontinued for the intratumoral injection procedure * NOTE: Heparin for line patency without detectable lab abnormalities in coagulation will be allowed * Corticosteroids =\< 2 weeks prior to registration, including oral, intravenous (IV), subcutaneous, or inhaled routes of administration * NOTE: Patients on chronic corticosteroids for adrenal insufficiency or other reasons may enroll if they receive less than 10 mg/day of prednisone (or equivalent) * NOTE: Exception allowed for patients who need prophylactic steroids prior to imaging for contrast allergies * Exception: Patients who received acute, low-dose systemic immunosuppressant medication or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy) are eligible for the study * Exception: Patients who received mineralocorticoids (e.g., fludrocortisone), corticosteroids for chronic obstructive pulmonary disease (COPD) or asthma, or low-dose corticosteroids for orthostatic hypotension or adrenal insufficiency are eligible for the study * History of myocardial infarction =\< 6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * Child Pugh class B or C cirrhosis of the liver * Previously received immune modulating therapies including but not limited to immune checkpoint inhibitors targeting PD-1 PDL-1 CTLA4, etc.; or prior dendritic cell therapy * Prior liver radiation, including radioembolization * GROUP 2 ONLY: Barcelona Clinic Liver Cancer (BCLC) stage D disease * GROUP 2 ONLY: History of untreated high-risk gastroesophageal varices * GROUP 3 ONLY: History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, or idiopathic pneumonitis, or evidence of active pneumonitis * Active tuberculosis * Treatment with therapeutic oral or IV antibiotics ≤ 2 weeks prior to registration * NOTE: Exception for patients receiving prophylactic antibiotics (e.g., to prevent a urinary tract infection or chronic obstructive pulmonary disease exacerbation) are eligible for the study * Prior allogeneic stem cell or solid organ transplantation * Treatment with a live, attenuated vaccine ≤ 4 weeks prior to registration, or anticipation of need for such a vaccine during study treatment, within 90 days after the final dose of tiragolumab, or within 5 months after the final dose of atezolizumab * NOTE: Patients being treated with chemotherapy (e.g., carboplatin, cisplatin, pemetrexed, paclitaxel, or gemcitabine) should not receive live vaccines * GROUP 3 ONLY: Acute Epstein-Barr virus (EBV) infection or known or suspected chronic active EBV at screening * NOTE: Patients with symptoms such as splenomegaly, fever, sore throat, non-malignant cervical lymphadenopathy, and/or tonsillar exudate, should undergo an EBV polymerase chain reaction (PCR) test to screen for acute infection or suspected chronic active infection. Patients with a positive EBV PCR test are excluded. Patients with positive Epstein-Barr virus (EBV) viral capsid antigen immunoglobulin M (IgM) test at screening are excluded * GROUP 3 ONLY: History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins * GROUP 3 ONLY: Known hypersensitivity to Chinese hamster ovary cell products or to any component of the atezolizumab or tiragolumab formulation * GROUP 3 ONLY: Known allergy or hypersensitivity to any component of the chemotherapy regimen the patient may receive during the study