I have some wool items dry cleaned, especially Pendleton wool shirts. Jackets or other items I will hand wash and line dry.
A variety of dry cleaning chemicals may be used by your dry cleaner. Historically, chlorinated solvents such as perchloroethene (or perchloroethylene), referred to as PCE, were used. These compounds are extrememly volatile and evaporate very quickly, leaving no odor. A lot of older mechanics used chlorinated solvents for parts cleaners.
However, some dry cleaners use naphtha or similar compounds which will leave a chemical odor for some period. Airing dry-cleaned fabrics out will usually strip volatile organic compounds completely.