Best job search strategy for someone graduating from university this April?

Take advantage of the Job Placement office at your university! They'll have postings for all sorts of job that employ recent graduates, and they probably have all sorts of resources for resume writing, interviewing skills, etc. You should be able to retain access to their services for a while after graduation, but be sure to stop in and find out what they have and how they can help you. You paid all that tuition,and you might as well take advantage of the resource while you can.