What is the difference between a crooked, twisted and deviated nose?

All the terms you mentioned are referring to the same thing.  A crooked, twisted and deviated nose are all the same.  Different maneuvers to straighten it will apply as each patient is different.

None of the terms that you have mentioned in your question serve as medical termniology, and they can often be used interchangeably among different surgeons of different training. The term "crooked nose" usually signifies that the nose is asymmetric largely to displacement of the nasal structure toward one side, in a very general sense. "Twisted nose"  is typically used for a nose in which the axis of the upper and lower nasal segments is not congruent; such as when the tip is strongly deformed compared to the nasal bridge that is oriented in the opposite direction. Deviation is also a general term often used to describe that a component of the nose is pushed to one side, and is often also applied to the nasal septum (e.g. right septal deviation). In the end, these three terms are strongly interchangeable, and it is more important to know which portion of the nose is affected rather than the specific term utilized. Best of luck!