Dear
Recruitment means hiring candidates for the present and(or) future vacancies in your organization. Recruitment may be done from various sources via advertisements, job portals like naukri.com, consultants, employee references etc.
Staffing means fitting the right candidte at the right job. It includes matching of skills and knowledge of the employees with the requirements of the job, i.e. Job specification and Job description. Staffing is next step after recruitment and selection and may be on the basis of performance in various tests, interview etc.
Outsourcing means getting any type of service in your business from some external source, like getting payrolls prepared for your employees by some chartered accountants(who is not working in your company and is not on your payrolls).
Regards
Ruchi