You are correct, if you combine Charge+Lunge or Cleave+Lunge (you cannot combine Cleave+Charge) your AC penalty is zero.
In short, for you, Cleave has a penalty of zero, Lunge has a penalty of zero, and Charge has a penalty of zero. Zero+Zero = Zero.
The feat Nimble Striker does not state to add up the total penalties and then reduce them by 2. That is what your GM is wanting to do.
The word "OR" in in the English language is unfortunately ambiguous, so any ruling would be technically correct based on one such interpretation. I would argue that the feat in this case applies three times, once for each ability as it is used, and thus eliminates all three penalties. I would be completely unsurprised if other GM's ruled otherwise. It may sound a bit obtuse, but interpreting "OR" as exclusive means that the feat could only be applied once if a charging-cleaving-lunge is used, thus leaving you with only one of the three penalties negated.
Yes, but in this particular case the "or" is pretty clearly being used to identify three different recipients of the effect that "You do not take a -2 penalty to AC when you use...".
It's a problem with the English language, that the word "OR" does not explicitly distinguish between its inclusive and exclusive forms, leaving the reader to interpret the meaning from context. Sadly, this means you end up arguing in circles if two readers come to different interpretations. I'm a programmer by trade, so understanding and clarifying the difference is actually really important to my day job. Maybe that makes me a little retentive when it comes to your more colloquial speech, but I've become very aware of the fact that people often don't think about the ambiguity in the word "OR"; what one person means and another interprets can be very different things.
I don't mean to be pedantic, and I agree with you on this ruling. Just saying that I wouldn't be surprised if there are a fair number of GM's out there who disagree.