Is this sentence correct?

[nathesh2011]

Neither of them are going to party on 10th October

[Barb_D]

Strict grammar will tell you that "neither" takes the singular form of the verb. Neither is.

However, in real life, we often use the plural.

On your exam, write "is." When you speak, don't worry about it very much.

[5jj]

Neither of them are going to a/the party on 10th October.

You'll hear Neither of them are going, but this is generally considered to be incorrect. You are safer with Neither of them is going

[5jj]

Well, you've heard it from both sides of the Atlantic, so it must be right.

[Barb_D]

And I totally missed the lack of an article before party!

[emsr2d2]

And I totally missed the lack of an article before party!

Unless "to party" was being used as a verb as it is quite frequently these days.

I'm going to party on Saturday night!
He's ready to party.