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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 in 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.

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.

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 in 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.)

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 in 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.

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 in downtown the night of Christmas Eve.

At least in American English, you can use a weekday as adverb, as in the following sentences:

We will try again Friday. (We will try again on Friday.)
See you Wednesday. (See you on Wednesday.)

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 in 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.)