Firstly, the GNU Project advises against using the term “MIT licence”, as it is ambiguous. See their comments on the Expat and X11 licences.
Now, on with the question:
I like to make my work public by using GPLv2-Only. This because its pretty clear with the copyleft: Use my work for whatever purpose you want, but if you change it or make it better, give it ...
A.) My-GPLv2-Only-Solution + MIT Lib
Yes, this is compatible. The combination must be licensed as a whole under the GPLv2, and the MIT parts do not impose any restrictions that make this as-a-whole licensing a problem. You can follow both licenses simultaneously, so they are compatible.
B.) My-GPLv2-Only-Solution + GPLv3+
This combination cannot be ...