The phrase "gave off odor" can be replaced with various synonyms depending on the context and intensity of the smell. For a strong and unpleasant odor, you can use "emitted a stench" or "exuded a foul odor." If the smell is more subtle, you could say "exuded a fragrance" or "emanated a scent." Another option is "released an aroma," which is often used in perfumes or cooking. In some cases, you could also simply say "smelled" or "had an odor." By using alternative phrases for "gave off odor," you can add variation and specificity to your writing while still effectively conveying the scent.