Do Pentecostal, Assembly of God, Churches have a service on Christmas Eve

Yes and no

Many of the Churches will. But it can also depend on local customs, church size and more. It has been some years, but they had them when I was a younger man.

My sister and one of my sons is Pentecostal. Fr_Chuck is correct -- size of congregation, local custom.

I live in the Bible Belt. A lot of Pentecostals here and they all have Christmas Eve services.