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Wiktionary gives the following definitions of дерзкий, наглый, and нахальный:

дерзкий:

1. brazen, impudent, impertinent, insolent, cheeky, pert




2. bold, daring, audacious

наглый:

impudent, impertinent, insolent, barefaced

нахальный:

1. impudent, insolent, impertinent




2. saucy, cheeky

I see imprudent, impertinent, and insolent in the definitions of each of the three Russian words - дерзкий, наглый, and нахальный.

However, looking at various examples of use of these three Russian words in the Internet, I got an intuitive feeling that they have pretty different connotations or flavors.

My question is this: What is the difference between дерзкий, наглый, and нахальный, especially when they describe a verbal response? I am especially curious to see examples of three different situations involving a verbal response to which, respectively, the following three expressions are most applicable: (1) это дерзкий ответ, (2) это наглый ответ, (3) это нахальный ответ.

UPDATE

Answers below made me confused, because my original impression was somewhat different. My original impression was that these three words denote the same thing and that the difference is only in the attitude or relationship of the speaker to the guy about whom the speaker is talking: Если наш - то дерзкий парень, а если их - то наглый нахал.

Imagine a guy who cuts a traffic jam line. Am I wrong in understanding that if it is your friend, you will say, "Mолодец, дерзко подрезал", and if he is not your friend and cuts the line right in front of you, your will react, "Нахал, нагло пролез"?

My original impression was partially based on this:

(1) Будем делать ракеты »: Путин дерзко ответил Трампу. (Source)

(2) Путин нагло пересек красную черту - реакция Порошенко на выдачу паспортов РФ в Украине. (Source)

As you see, a Russian says about Putin using the word дерзкo, and a Ukrainian - using the word нагло. I even found а Youtube video entitled "Путин дерзко ответил наглому украинцу." This title seems to perfectly tell who the author is with.

Is my impression wrong?

Those the words indeed have different connotations. Ответ can be дерзкий, наглый but нахальный usually refers to a person, his character and sounds odd when used with ответ, but not strictly wrong.

Дерзкий is usually a positive word, closer to courageous, daring, bold, but also cheeky, audacious. Журналист задавал певице дерзкие вопросы, от которых она краснела.

Наглый is more negative or neutral. Implies being selfish and possibly inconsiderate of others. Он нагло пролез к кассе без очереди.

Нахальный is always negative. A stronger meaning than наглый, implying the person is more of a nuisance to others, offensive, etc., where as наглый might just mean impolite or breaking social conventions. Он нахально оставил машину на тротуаре, загородив вход.

involving a verbal response

1. 
   дерзкий has only negative connotations: provoking, aggressive, incendiary (but truly can be positive in a different context)


2. 
   наглый is the same but more expressive, I would also say it sounds more informal


3. 
   нахальный is, first of all, marked as informal in dictionaries and supposes more arrogance, shamelessness and the lack of considerateness.

To sum up: these three words mean the same thing, while their expressiveness grows and the formality drops.
All three can be applied to either actions (responses) or people.