Im from England it might be different in america but here 'Nasty' isnt quite the same as Dirty. We would say 'Your hands are dirty' Or 'your hands are filthy' To say 'Your hands are nasty' Could be seen as an insult, like you are saying the actual physical appearance of your hands isn't nice. Nasty kind of has the same meaning as disgusting. For example you could say 'this food tastes Nasty' Nasty can also mean bad or say if you described a person as 'Nasty' they would be a mean person or a rude person.

dirty means not clean like if i have been sweeping the floor i can't eat with my hands before washing them because they are dirty(not clean). nasty means dirty but disgustly, i mean dirty but in an unpeasant way. like if i have been playing in the mud made myself dirty; hands, face and clothes, i think i'll be nasty this way.

Nasty = horrible dirty = unclean They are NOT interchangeable.

*unpleasant