Yeah, Old Dominion University does provide scholarships based on merit. Here are some of them:

The James L. Bugg Scholarship
Minimum Criteria: Participation in extracurricular activities and community service and demonstration of top academic achievement
Separate application needed: No

The Clifford and Ann Cutchins, III Dominion Scholarship
Minimum Criteria: Minimum 3.8 cumulative grade point average, rank in the top 10 percent of their graduating class, and score 1280 or better on the SAT
Separate application needed: No

The Robert L. and Geraldine E. Fodrey Alumni Association Memorial Scholarship
Minimum Criteria: Minimum 3.8 cumulative grade point average, rank in the top 10 percent of their graduating class, and score 1280 or better on the SAT
Separate application needed: No

Old Dominion University provides aids at an average of 12247 per student meeting 49% of students need. 96% of students with need receive financial aid at an average of 7999 need-based grant. They also provide other scholarships including ROTC Scholarships and TEACH Grant.