Is it permissible to describe a person as loathsome based on the observation of unpleasant odors emanating from them in certain situations, or does this description contradict Allah being Beautiful and loving beauty?

It is not permissible to describe someone as "detestable," as this falls under the category of forbidden backbiting (gheebah), which is mentioning about your brother what he dislikes, even if what you said about him is true. The Prophet, peace and blessings be upon him, said to Aisha, may Allah be pleased with her, when she described Safiyyah as deficient: "You have uttered a word that if it were mixed with the water of the sea, it would contaminate it."