There are several synonyms for the phrase "gives off odor." Some common alternatives include emitting a smell, exuding a scent, radiating an aroma, releasing a fragrance, projecting a stench, or giving out an aroma. Depending on the context, other words such as reeking, stinking, or smelling foul may also be appropriate. When describing a pleasant smell, alternatives may include emanating a pleasant fragrance, wafting a delightful scent, or breathing out an alluring aroma. Regardless of the specific words chosen, the goal is to convey the concept of a noticeable and distinct smell emanating from a particular source.