Which of the following prepositions would be most appropriate to be used before Wednesday night and the night of Christmas Eve when referring at exactly during these time(s) (not before or after)?
You don’t typically use a preposition there, but if you must, on is the correct one, because you are basically referring to a day, or a general time period within a day:
on Wednesday (night)
on (the night of) Christmas Eve
At is definitely not correct, because generally we use at for times, not dates. In is technically correct as well, because “in the night” means “during the night” or “at nighttime”, but you would still use on to attach a specific date:
I heard a strange sound in the night on Christmas Eve.
In the examples you make, there is no need to use any preposition.
We can get together Wednesday night.
Since there was nothing I could do, I wandered downtown the night of Christmas Eve.
At least in American English, you can use a weekday as adverb, such as in the following sentences:
We will try again Friday. (We will try again on Friday.)
See you Wednesday. (See you on Wednesday.)
This usage is reported to be chiefly North American, from the OED.
That's going to be rather a long list. Just considering prepositions beginning with a and b, here are some example phrases which would be appropriate:
The same list will be appropriate for "the night of Christmas Eve".
