Sterilize 5 (1 pint) jars with lids and rings. Keep hot.
Place beets into a large pot and fill with enough water to cover. Bring to a boil and cook until beets are tender enough to pierce with a fork, but not mushy. Drain and cool, reserving 2 1/2 cups of the water from the beets. When beets are cool enough to handle, peel and trim the ends. Cut into wedges or chunks if desired and pack into hot jars.
While the beets are cooking, combine the sugar, vinegar, pickling salt, lemon juice and clove oil in a large saucepan or pot. Bring to a boil. Pour the hot brine over the beets in the jars to within 1/4 inch of the top. Wipe the rims with a clean towel and seal with lids and rings. Set at room temperature for 24 hours, then store in the refrigerator. Wait a few days before eating to allow beets to soak up the flavor.