bend & crook & curve are different parts of speech.
bent & crooked & curved are adjectives.
bent means "not straight", so it can be a gentle curve or a sharp bend. It can mean intentionally so, or supposed to be straight and is now distorted.
crooked means "not straight" in the sense of perhaps imperfect, or out of alignment, or out of shape for something that maybe should be straight.
curved means "not straight"" in the sense of usually a gentle curve, not an abrupt corner.