Vaccine Therapy in Treating Patients With Advanced Adenocarcinoma of the Prostate (Prostate Cancer)

Inclusion Criteria: * Histologically proven adenocarcinoma of the prostate with evidence of metastatic disease including any of the following: * Lymph node positive and prostate-specific antigen (PSA) at least 10 ng/mL * Bone scan positive and PSA at least 10 ng/mL * Prior radical prostatectomy with rising PSA and PSA at least 2 ng/mL * Prior radiotherapy and PSA at least 10 ng/mL * Prior cryosurgery and PSA at least 10 ng/mL * PSA criteria does not apply to patients who are assigned to group B of this study and were previously treated on vaccine trial DFCI-96079 * No symptomatic metastatic disease (no bony pain) * Complete HLA typing required * Performance status - ECOG 0 or 1 * WBC greater than 2,000/mm\^3 * Platelet count greater than 100,000/mm\^3 * Bilirubin less than 2.0 mg/dL * SGPT less than 4 times upper limit of normal * Creatinine less than 4.0 mg/dL * No altered immune function such as eczema * No autoimmune diseases such as the following: * Autoimmune neutropenia, thrombocytopenia, or hemolytic anemia * Systemic lupus erythematosus, Sjögren's syndrome, or scleroderma * Myasthenia gravis * Goodpasture's syndrome * Addison's disease, Hashimoto's thyroiditis, or active Graves' disease * HIV negative * No allergy or untoward reaction to prior vaccinia (smallpox) vaccination * No hypersensitivity to eggs * No prior or concurrent extensive eczema or skin disorders (e.g., extensive psoriasis, burns, impetigo, or disseminated zoster) * No other concurrent serious illness * No active infection requiring antibiotics until infection has cleared and antibiotics have been stopped for at least 3 days * Fertile patients must use effective contraception * No close contact or household contact with the following high-risk individuals for at least 2 weeks after each vaccination: * Children under age 5 * Pregnant or nursing women * Individuals with prior or concurrent extensive eczema or other eczematoid skin disorders * Individuals with other acute, chronic, or exfoliative skin conditions (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne, or other open rashes or wounds) * Immunodeficient or immunosuppressed individuals (by disease or therapy) such as those with HIV infection * See Disease Characteristics * See Endocrine therapy * Prior vaccinia (smallpox) immunization required * No other concurrent biologic therapy (e.g., interferon or interleukin) for cancer * No prior chemotherapy for metastatic disease * No concurrent anticancer chemotherapy * No prior hormonal therapy for metastatic disease * Prior neoadjuvant hormonal therapy followed by prostatectomy or radiotherapy allowed * Patients previously treated with recombinant vaccinia-PSA vaccine may have hormonal therapy since discontinuing that treatment (Group B) * No concurrent hormonal therapy or steroids * See Disease Characteristics * See Endocrine therapy * No concurrent radiotherapy * See Disease Characteristics * See Endocrine therapy * No prior splenectomy * At least 3 days since prior antibiotics * No concurrent immunosuppressive treatment (e.g., after organ transplantation)