Separate the garlic heads into individual cloves and peel. To make peeling easier, blanch the cloves in rapidly boiling water for about 30 seconds, then immediately transfer them to cold water — the skins will slip right off.
In a non-reactive pot, combine the vinegar, water, salt, sugar, and oregano. Bring to a boil, then reduce heat and simmer for 1 minute.
Add the peeled garlic cloves to the pot and simmer for 1 more minute.
Pack the garlic cloves into half-pint jars, leaving ½ inch of headspace.
Ladle the hot pickling liquid over the garlic, maintaining ½ inch of headspace. Remove air bubbles, wipe the jar rims clean, and apply the lids.
Process in a water bath for 10 minutes, adjusting for your altitude. Let jars cool undisturbed for 12–24 hours, then check the seals.