Induction Chemotherapy With ACF Followed by Chemoradiation Therapy for Adv. Head & Neck Cancer

Inclusion Criteria:

* Patient must have selected stage III or IVa/b head and neck squamous cell carcinoma (HNSCC); all patients must have T2-T4 primary tumors; (patients with T1 tumors will be excluded); although most of these patients will have regional nodal disease, patients with no nodal disease will also be eligible
* Patient must have disease at the oropharynx, hypopharynx, larynx, or oral cavity sub-sites
* Patient must have measurable disease defined as lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 10 mm with CT scan
* Patient must be \>= 18 years of age.
* Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2
* Patient must have adequate bone marrow and organ function as defined below:

  * Absolute neutrophil count (ANC) \>= 1500/mcL
  * Platelets \> 100,000/mcL
  * Hemoglobin \> 9.0 g/dL
  * Total bilirubin =\< 1.5 mg/dL
  * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 2.5 x upper limit of normal (ULN)
  * Alkaline phosphatase =\< 2.5 x ULN
  * Serum creatinine \< 1.8 mg/dL
* Women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry, for the duration of study participation, and for 3 months after completing treatment. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately
* Patient must be able to understand and willing to sign an Institutional Review Board (IRB)-approved written informed consent document
* Patient with uncontrolled diabetes or fasting blood glucose level of greater than 200 mg/dL will be eligible for enrollment but will not be evaluable for PET imaging

Exclusion Criteria:

* Patient must not have had prior chemotherapy, prior epidermal growth factor receptor (EGFR) targeted therapy, or prior radiation therapy for HNSCC
* Patient must not have disease at the nasopharyngeal, sinus, or other sub-site not specified in the inclusion criteria; patient must not have unknown primary squamous cell carcinoma of the head and neck
* Patient must not have a history of prior invasive malignancy diagnosed within 3 years prior to study enrollment other than local stage non-melanoma skin cancer
* Patient must not be receiving any other investigational agents
* Patient must not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to any of the agents used in this study
* Patient must not be taking cimetidine or allopurinol. If currently taking either of these medications, patient must discontinue for one week before receiving treatment with nab-paclitaxel
* Patient must not have an uncontrolled intercurrent illness including, but not limited to, ongoing or active serious infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or serious psychiatric illness/social situations that would limit compliance with study requirements
* Patient must not be pregnant and/or breastfeeding; a negative serum or urine pregnancy test is required at screening for all female patients of childbearing potential
* Patient must not be known to be human immunodeficiency virus (HIV)-positive on combination antiretroviral therapy because of the potential for pharmacokinetic interactions with the study agents; in addition, these patients are at increased risk of lethal infections when treated with marrow suppressive therapy; appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated
* Patient must not have peripheral neuropathy \> grade 1