153Sm-EDTMP With or Without a PSA/TRICOM Vaccine To Treat Men With Androgen-Insensitive Prostate Cancer

* INCLUSION CRITERIA: A. Histopathological documentation of prostate cancer confirmed in the Laboratory of Pathology at the National Institutes of Health (NIH) Clinical Center, National Institutes of Health (NIH), the National Naval Medical Center, or Walter Reed Army Medical Center; or participating Institute's Department of Pathology prior to starting this study. If no pathologic specimen is available, patients may enroll with a pathologist's report showing a histologic diagnosis of prostate cancer and a clinical course consistent with the disease. B. Must have metastatic castration resistant prostate cancer (CRPC) with at least 2 bone lesions consistent with prostate cancer metastasis and progressive disease (2 rising PSA values separated by at least one week, new or enlarging lesions consistent with prostate cancer, or clinical progression) on docetaxel for metastatic prostate cancer or inability to tolerate docetaxel. C. Life expectancy greater than or equal to 6 months. D. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. E. No systemic steroid or steroid eye drop use within 2 weeks prior to initiation of experimental therapy. F. Hematological eligibility parameters (within 16 days of starting therapy). * Granulocyte count greater than or equal to 1,500/mm\^3 * Platelet (PLT) count greater than or equal to 100,000/mm\^3 * Hemoglobin (Hgb) greater than or equal to 10 Gm/dL (Transfusion may be given to accomplish this) G. Biochemical eligibility parameters (within 16 days of starting therapy) -Hepatic function: aspartate aminotransferase (AST) and alanine aminotransferase (ALT) less than 2.5 times upper limit of normal; bilirubin less than 1.5 mg/dL OR in patients with Gilbert's syndrome, a total bilirubin less than or equal to 3.0 mg/dL. H. No other active malignancies within the past 12 months (with the exception of nonmelanoma skin cancers or carcinoma in situ of the bladder and treated with curative intent) or life-threatening illnesses. I. Willing to travel to the National Institutes of Health (NIH) or participating Institute for follow-up visits. J. 18 years of age or greater. K. Able to understand and sign informed consent. L. Agree to use adequate contraception prior to study entry and for at least 4 months following the last vaccine injection. M. Patients must remain on medical castration therapy with testosterone-suppressing therapy (e.g., gonadotropin releasing hormone (GnRH) agonist), unless they have had surgical castration. N. Patients must have recovered from acute toxicities related to prior therapy or surgery. For chemotherapy, typically this is 3 to 4 weeks. O. Patients who are incontinent of urine should be willing to undergo bladder catheterization to minimize the risk of radioactive contamination of clothing, bed linen, and the patient's environment. P. Concurrent treatment with bisphosphonates is allowed. If bisphosphonates have been given within 2 weeks prior to planned (153)Sm-EDTMP, then a 99Tc whole-body scintigraphy (bone scan) will be performed to confirm uptake into lesions. Bisphosphonates will not be given within 48 hours after (153)Sm-EDTMP administration. Q. Serum creatinine less than or equal to 1.5 times upper limit of normal OR creatinine clearance on a 24-h urine collection of greater than or equal to 60 mL/min. EXCLUSION CRITERIA: A. Patients should have no evidence, as listed below, of being immunocompromised: * Human immunodeficiency virus (HIV) positivity due to the potential for decreased tolerance and risk for severe side effects. * Hepatitis B or C positivity. * Concurrent use of topical steroids (including steroid eye drops) or systemic steroids. This is to avoid immunosuppression which may lead to potential complications with vaccinia (priming vaccination). Nasal or inhaled steroid use is permitted. B. Patients should have no autoimmune diseases that have required treatment, such as Addison's disease, Hashimoto's thyroiditis, systemic lupus erythematosus, Sjogren's syndrome, scleroderma, myasthenia gravis, Goodpasture's syndrome, or active Grave's disease. Patients with a history of autoimmunity that has not required systemic immunosuppressive therapy or does not threaten vital organ function, including central nervous system (CNS), heart, lungs, kidneys, skin, and gastrointestinal tract (GI) tract, will be allowed. C. History of allergy or untoward reaction to prior vaccination with vaccinia virus or to any component of the vaccinia vaccine regimen. Note: prior vaccination with vaccinia is not required. D. Do not administer the recombinant vaccinia vaccine if the recipient or, for at least 3 weeks after vaccination, their close household contacts (close household contacts are those who share housing or have close physical contact), are persons with active or a history of eczema or other eczematoid skin disorders; those with other acute, chronic or exfoliative skin conditions (e.g., atopic dermatitis, burns, impetigo, varicella zoster, severe acne, or other open rashes or wounds) until condition resolves; pregnant or nursing women; children 3 years of age and under; and immunodeficient or immunosuppressed persons (by disease or therapy), including HIV infection. E. Serious intercurrent medical illness (e.g., one that requires treatment) which would interfere with the ability of the patient to carry out the treatment program, including, but not limited to, inflammatory bowel disease, Crohn's disease, ulcerative colitis, or active diverticulitis. F. Patients with a history of cardiomyopathy or symptomatic congestive heart failure (unless stable on treatment), symptomatic arrhythmia not controlled by medication. Unstable atherosclerotic heart disease (e.g. unstable angina) who require active intervention and history of myocardial infarction or embolic stroke within the past 6 months. G. Patients with cardiac disease who have fatigue, palpitation, dyspnea or angina with ordinary physical activity (New York Heart Association class 2 or greater) are not eligible. H. Patients with a history of congestive heart failure or who have objective evidence of congestive heart failure by physical exam or imaging are not eligible, unless the underlying cause has been treated and patient has documented normal ejection fraction. I. Patients with pulmonary disease who have fatigue or dyspnea with ordinary physical activity are not eligible. J. Concurrent chemotherapy. K. No brain metastasis or history of seizures, encephalitis, or multiple sclerosis. L. Serious hypersensitivity reaction to egg products. M. Prior splenectomy. N. Contraindicated in patients who have known hypersensitivity to EDTMP or similar phosphonate compounds. O. Patients with symptomatic soft tissue disease or parenchymal disease will be excluded. P. Radiation therapy to bone within 4 weeks of study entry. Q. Patients previously treated with (153)Sm-EDTMP will be excluded. R. Patients requiring urgent local radiotherapy or orthopedic stabilization.