These all seem to be used for explanation... when do you use one over the other? Could you offer some examples?
To clarify about の, I am talking about its use in providing information, like, 昨日、デパートに行ったんです
I can think of two uses of の that the OP could be referring to:
In terms of わけ, わけ functions as a reason within a sentence or conversation. So we often would translate it in Cf. そこまでボールを投げたわけがない。 as "there's no way I can hit a ball that far". There's no possibly way of hitting it that far, i.e. there is no rhyme or reason enabling that.
理由 on the other hand is properly speaking reason or reasons. 三つの理由があります. (There are three reasons). If you prefer, you can think of 理由 as "logical reason" and in general you shouldn't just drop this into the middle of an explanation that isn't founded on reasoning.