"What the hell?" is a toned down variant of "what the fu**" and can be considered offensive in some formal contexts. My question is more about other expressions like "hell no!". Is it impolite or offensive as well?
"Hell no" is a way of conveying strong emphasis in one's disagreement. As Berker mentioned, "politeness" is context dependent. You haven't mentioned any example usages in your question, so we are all left imagining where you might use this, trying to determine whether or not your utterance would cross the boundaries of politeness:
Let's saying I'm talking with a co-worker who I have worked quite closely with in the past.
How was your weekend?
It was okay. My daughter has had a boyfriend for a couple of weeks now, they wanted to know if they could go camping together on Saturday night.
With a group?
No, by themselves.
What did you tell her?
I told her, "Not only 'No,' but 'Hell, no.'"
That's an idiomatic way of saying there was absolutely no way I was going to let my daughter go camping with her boyfriend: not at her age, not at that stage of their relationship, not when I knew so little about her new boyfriend. I doubt my coworker would find the wording impolite, unless he was prone to take umbridge at expressions with even a modicum of religious overtones.
Now, let's move the conversation to another place in my office, where someone is asking if I've seen the monthly report yet:
Have you seen the monthly report yet?
Oh, is it out?
Yes, it came out yesterday. Did you see it?
Hell, no, I haven't seen it. I just told you, I didn't even know it had been released yet.
That remark would be considered rude – not because of the word hell, but because it's said in a much sharper tone than was necessary. My coworker was merely being polite, and I started acting like a jerk.
You use "Hell, no" (or "Hell, yes") when you want to convey strong emphasis. "Hell, yes, I'm glad Manchester won the game" works just fine when two football fans are talking about sports. "Hell, yes, I'm glad it's Friday" might be overdoing it when someone greets you at the office; I'd reserve that kind of talk for only my closest associates. Hell, yes, I'm glad to see you" is almost assuredly too much if I am meeting a business associate for the first time, but it might work just fine if I'm meeting my brother at the airport, and I haven't seen him for two or three years.
Hell no is an informal emphatic no, and many people would not find it any more offensive than similar slang terms such as "Oh my God!", which are widely used and normally not intended offensively.
That said, Hell no and other such slang terms are not generally suitable for formal occasions or when in polite company; you would be well advised to avoid such language in formal settings, or with people that you do not know (unless you have heard them use such language themselves).
When in doubt, you can always substitute the term definitely not which carries the same meaning.
Is it impolite?
Offensiveness of the context is arguable by how you use it but it surely is impolite;
- It's always impolite to remind people the things that makes them feel bad.
- "Hell" is a definition for the base of bad things, where everything is negative.
- "No" is a negative answer which people doesn't wants to hear.
When these two comes together creates an expression which includes the meaning "Even while in hell and it's my only chance to be saved, I won't accept it." which is an extremely harsh way to say no. Hurting the feelings of the person that expects a positive answer.
Is it offensive?
I would say it is based on how you say it. A serious impression on your face with a tick voice would create an offensive reply while with a smiling face and a mocking voice would create a friendly reply.