If the vote was 3-2 or 4-3 or 151-150 that is a majority of one. A majority occurs when more than half the votes go a certain way and "of one" or "of two" or "of x" refers to the number or margin that was in excess of half of the votes. I hope that helps.

I don't think I've ever heard anyone say "majority of two", but I can tell you that "majority of one" is something one would only say ironically or sarcastically. Depending on the surrounding context, I suppose it could mean either of two different things: (1) the speaker is drawing attention to the fact that nobody else is in agreement with the "one" the speaker is talking about, and perhaps that person is delusional and thinks others agree with him; (2) the "one" the speaker is referring to is the only person whose opinion actually matters. Without more context, I would guess it's the second one. For example, a chairman of a department at a university told me once that the opinion of the provost counted more than the opinions of the entire rest of the faculty combined. He was a "majority of one".