To dress is an intransitive verb,* so it doesn't require an object, whereas to wear is a transitive verb, so it requires an object. So you can say:
She dresses differently than ordinary people do.
She wears odd/weird/unusual clothes. <-- "clothes" is the object She dresses oddly/weirdly/unusually.
Her fashion sense is unique/odd/weird/unusual.
She has a unique/odd/weird/unusual sense of style.
*except in the case of dressing someone else, e.g. a mother who dresses her child.