Radiation Therapy and Cisplatin With or Without Cetuximab in Treating Patients With HPV Positive, KRAS-Variant Stage III-IV Oropharyngeal Squamous Cell Carcinoma

Inclusion Criteria:

* Written informed consent obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluation
* Newly diagnosed, untreated, biopsy-proven HPV+ squamous cell carcinoma of the oropharynx. Cytologic diagnosis from a cervical lymph node is sufficient in the presence of clinical evidence of a primary tumor in the oropharynx. Clinical evidence should be documented, may consist of palpation, imaging, or endoscopic evaluation and should be sufficient to estimate the size of the primary (for T stage). HPV-positivity will be defined as tumors that are p16-positive by immunohistochemistry
* Selective stage III-IV disease (T3-T4 or N2-N3 disease) by American Joint Committee on Cancer (AJCC) 8th edition as determined by a computed tomography (CT) scan or magnetic resonance imaging (MRI) of the head and neck, CT neck, chest, abdomen, pelvis or a PET =\< 6 weeks of registration
* Confirmation of KRAS-variant status as assessed by genotyping from a cheek swab sample at MiraDx
* Lifetime cumulative smoking history of \< 10 pack-years. The cumulative total of the number of pack-years during each period of active smoking is the lifetime cumulative history

  * Note: Investigators are discouraged from enrolling patients with a history of very sustained use (such as several years or more) of non-cigarette tobacco products alone given that the effect of non-cigarette tobacco products on the survival of patients with p16-positive oropharyngeal cancers is undefined
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 ? 1 within 60 days prior to registration
* Hemoglobin \>= 9 g/dL (5.58 mmol/L) (within 2 weeks prior to registration)
* Absolute neutrophil count (ANC) \>= 1500/uL (cells/mm\^3) (within 2 weeks prior to registration)
* Platelet count \>= 100,000/uL (cells/mm\^3) (within 2 weeks prior to registration)
* Total bilirubin =\< 1.5 mg/dL (25.65 umol/L) or =\< 3.0 mg/dL if the patient has a history of Gilbert?s disease (within 2 weeks prior to registration)
* Aspartate transaminase (AST)/alanine transaminase (ALT) =\< 2 x the institutional upper limit of normal (ULN) (within 2 weeks prior to registration)
* Serum creatinine =\< 1.5 x institutional ULN OR creatinine clearance (measured via 24-hour urine collection) \>= 50 ml/min (that is, if serum creatinine is \> 1.5 times the ULN, a 24-hour urine collection to calculate creatinine clearance must be performed) (within 2 weeks prior to registration)
* Female subjects must either be of non-reproductive potential (i.e., post-menopausal by history: \>= 60 years old and no menses for at least 1 year without an alternative medical cause, OR history of hysterectomy, OR history of bilateral tubal ligation, OR history of bilateral oophorectomy) or must have a negative serum pregnancy test within 7 days prior to enrollment
* Female subjects of child bearing potential and male subjects with partners of child bearing potential must agree to adequate contraceptive measures (hormonal or barrier methods) during treatment and for 2 months after the last dose of cetuximab
* Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment, scheduled visits, and examinations including follow up

Exclusion Criteria:

* Patients with biopsy-proven metastatic, HPV-negative, KRAS-variant negative, or recurrent head and neck squamous cell carcinoma (HNSCC)
* Patients with primary site of tumor outside of the oropharynx, specifically of the oral cavity, salivary glands, nasal cavity, paranasal sinuses, larynx, hypopharynx, or nasopharynx
* Patients with prior radiation therapy (RT) that would result in overlap of radiation therapy treatment fields (superficial x-ray of skin lesions excluded)
* Gross total excision (ex. tonsillectomy) of the primary tumor; however, partial removal of the tumor to alleviate an impending airway obstruction does not make the patient ineligible. Initial surgical treatment, excluding diagnostic biopsy of the primary site or nodal sampling of neck disease, as well as radical or modified neck dissection is not permitted
* Prior systemic chemotherapy or biologic therapy for the study cancer; note that prior chemotherapy or biologic therapy for a different cancer is allowable
* Prior therapy that specifically and directly targets the EGFR pathway
* History of another primary invasive malignancy except for:

  * Malignancy treated with curative intent and with no known active disease \>= 3 years before the first dose of study drug and of low potential risk for recurrence
  * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease
  * Adequately treated low risk prostate cancer without evidence of disease
  * Adequately treated carcinoma in situ without evidence of disease e.g., cervical cancer in situ, and ductal breast carcinoma in situ (DCIS)
* History of infusion reaction or hypersensitivity to cetuximab OR allergic reactions attributed to compounds of chemical or biologic composition similar to those of cetuximab
* Documented uncontrolled intercurrent illness or co-morbidity including, but not limited to, ongoing or active bacterial or fungal infection requiring intravenous antibiotics, uncontrolled congestive heart failure, cardiomyopathy, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition, or psychiatric illness/social situations that would limit compliance with study requirements or compromise the ability of the subject to give written informed consent
* Female subjects who are pregnant or breastfeeding as well as male or female patients of reproductive potential who are not employing an effective method of birth control
* Patients with clinically relevant coronary artery disease or history of myocardial infarction in the last 12 months or high-risk of uncontrolled arrhythmia or uncontrolled cardiac insufficiency
* Patients with uncontrolled or poorly-controlled hypertension (\> 180 mmHg systolic or \> 130 mmHg diastolic)
* Any condition that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results
* Involvement in the planning and/or conduct of the study