There are specific patterns that are more common for certain uses than others, and choosing the wrong verb would sound a bit off to a native speaker.
Example 1: When using "I was just wondering," you start off in the past tense, so might, which is historically the past tense of may, "sounds better" here. It is sequence of tenses. Also, you're asking for a favor; and might is just a little more polite. Additionally, using may can be taken for "possibility in the future" rather than "willingness to fulfill a request."
Example 2: When used in this kind of a sentence, may expresses an indirect imperative, or a wish on the part of the speaker. It shares some semantic overlap with let: May the force be with you; Let the games begin.
Example 3: Here, there is a lot of overlap between may and ** might**, as an expression of possibility, but You may well be right is a set expression, with over 20 times the frequency in 2000 as You might well be right. The key element to making it a set expression is the word well. Take it out, and may still outperforms might, but only by about 2 to 1 rather than 20 to 1.
All that being said, I would hesitate to say that the other choice is egregiously wrong in Examples 1 or 3. In Example 2, you pretty much must use may.