Move the time earlier... young children get cranky after dinner (especially when they are all inside). Not sure why you are locked into a time.
I would suggest sending out an email or another "flyer" announcing a new time and "please no gifts". Yes, people will bring you something small for your new home (bottle of wine-ish), but at least this way they won't feel the need to go out and "shop".
As for activities for very small children, that's tough. We have gotten in the habit of hiring a sitter to be at our home when we have parties so that our son and the other children are supervised and have someone to "lead" games.
You are now talking about a pretty broad age-range so I would hire someone and just ask that person to entertain the kids. Make sure that there are plenty of books, play doh, crayons, paper, simple craft supplied etc available. If there are things you don't want "touched" or could be broken, put them away. Have "kid food" and "drinks" ready and make sure that you have a coffee table cleared-off so the kids have a sturdy place to eat.
If you move the party earlier and hire a sitter to "kid wrangle", they could go outside. I saw a great idea in a magazine and tried it with my son and neighbors and it was a huge hit... we put water color (washable) paints heavily diluted in squirt bottles and let the kids "paint" the snow. They had a blast and the color washed off of their clothes and hands easily.