Dinner on Christmas Eve-
There is a very similar thread running right now about restaurants open on Christmas Day, so you might check out some of those recs (in terms of where you might find the info on which places are open). I would think you would have a lot more options on Christmas Eve than on Christmas Day.
I think it would be helpful for you to scan the Board a bit to see what restaurants look interesting to you then check some of the websites that were suggested in the other post to see if they are open.
Price point? Where are you coming from - are there types of foods you can't get there or have too much of that you want to avoid in Portland?