Hi
Every possible scale can be used. There are several ways to harmonize a melody that fits in a scale, mainly two (but there are more):
1. Using chords formed ONLY by notes of the scale.
2. Using additional chords that with notes laking in the scale. This is possible because melody usually prevails. In some cases the chords we can use from only the notes of the scale are not useful.
One important decision, sometimes difficult to take, is which chords are the most important (the primary chords).
The first is the tonic. In your scale it would be A - C# - E. If your tonal centre is other, let's say D, the tonic chord would be D - F - A and you would be using the IV mode of this scale.
I think it is a mistake, when using this artificial scales (or the exotic ones), to try to find functional relationships as we do in tonal music (tonic-subdominants-dominants). I think these scales should be treated as modal.
So we will not have subdominants nor dominants chords. Besides the tonic chord, we have to find cadential chords. There are some methods to establish them, but this would be too long... The best is to play and try.
Regarding melody, it is important to use all the notes soon, particularly the ones that give personality to the scale.
What I don't understand is why you have limited the chords to the ones you mentioned. As an octatonic scale, you can built lots of chords.
There are many other possible ones, why not to use them?:
A - C# - E - G
A - C# - E - G#
B - D - F - A
etc...