Combine cider or juice, frozen sliced strawberries, the 4 inches stick cinnamon, and cloves in a large saucepan. Bring to boiling and reduce heat. Cover and simmer for 10 minutes. Strain through a sieve lined with 100-percent-cotton cheesecloth.
To serve, pour cider mixture into eight heatproof glasses or cups. Garnish each serving with a cinnamon stick and a fresh strawberry or apple slice, if desired. Makes 8 (8-ounce) servings.