What is a health care staffing agency? Healthcare Staffing Agency As a dedicated health care professional, you want choices in your profession - choices that suit your lifestyle, your professional goals and your personal needs. And, you want a health care staffing company that delivers on its promises - excellent compensation, personalized service and support every step of the way.What are medical staffing companies? Ohio Medical Staffing is a regional medical staffing company providing Physical, Occupational, and Speech Therapy services on a contract basis to clients in a wide variety of clinical settings, including home health, skilled nursing, acute care and outpatient.What is medical staffing? medical staff. physicians and dentists who are approved and given privileges to provide health care to patients in a hospital or other health care facility. Medical staff personnel may work full time or part time and may be employed by the facility or granted admitting privileges to practice.