Heat cooking oil in a medium saucepan. Cook onion, gingerroot, and garlic in hot oil until tender but not brown.
Stir together the sugar and cornstarch. Stir into saucepan. Stir in vinegar, lemon juice, mustard, allspice, and cloves until well blended. Stir in the peaches and cherries or raisins. Cook and stir until slightly thickened and heated through. If desired, stir in almonds. Serve warm as an accompaniment to ham. Makes about 2 cups.