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You can localize in multiplicative set, for example odd integers (here You are right), but if one sais "to localize in prime ideal" he means to localize in a multiplicative set consisting of all elements not in a given prime ideal. So "to localize at the prime ideal (2)" means exactly "to localize using multiplicative set of odd numbers".
A distinction should be drawn between the precise meaning of these terms and the popular meaning. In the latter case, "average" nearly always refers to the arithmetic mean, but more precisely it refers to a "typical value", or with more jargon, a "measure of central tendency". Thus any mean, or mode, or median, is an average. (Though the mode, in particular, can be anything but central.)
Again, "mean" without qualification usually refers to the AM, but there are any number of different means which can be calculated from a set of figures, the commonenest are maybe the geometric and harmonic varieties.