Why are there no Oe or Ae stars? The unique characteristics of Be stars are mainly because of their circumstellar discs.
I wonder what makes Be stars special that only they have unique characteristics?
Which kind of stars have discs generally?
Why are there no Oe and Ae stars?
Well, there might be.

I strongly disagree with your statement that circumstellar discs are what differentiate B(e) stars from other related stars. In fact, there are four primary criteria for stars that satisfy "the B(e) phenomenon":


Strong emission lines in the Balmer series
Emission of lines of certain (low ionization) metals such as Fe II
"Forbidden emission lines" in the visible part of the electromagnetic spectrum such as O I
Hot circumstellar dust


The dust is not the key to the B(e) phenomenon, though it can change the spectrum slightly.

HAeB(e) stars are a class of stars (and a subclass of B(e) stars) related to Herbig Ae/Be stars, which have not yet left the main sequence. There are additional criteria that a star must satisfy to be considered an HAeB(e) star, too. These stars can be of spectral type A, meaning that you can have B(e) stars that are not of spectral type B, if you use a certain definition.

This answer is based largely on Lamers et al. (1998), a fascinating paper on the classification of B(e) stars.