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.