What causes vaginal itch without odor, discharge, or rash?

Yeast infection? Yeast infection is the most likely explanation. Contrary to popular opinion, yeast infections usually cause little discharge and do not cause abnormal odor. See a doctor. Or you could try an over the counter yeast medication, active ingredient ending with "azole" (miconazole, clotrimazole, etc). But for sure get professional care if it doesn't help within a week.