There are noises in the walls of my home, mainly a lot of movement which is fairly loud. I have worked with exterminators and is now working with a wild life remover. Nothing is working. The outside of my home according to the wild life remover has been completely sealed. But I still have something moving in the walls. They seem to be moving along the lines where the duct work is. They are between the floors of my home and is able to come up into the kitchen walls and my bedroom walls near the duct work. The wild life remover said I had a flying squirrel which entrance point was sealed. Now he thinks I have mice, but we are not seeing any evidence of them. Traps have been set and nothing was caught. What do you think it could be? I did see acorns around a possible entrance point by my front stairs.

Yes, mice.
I'm not buying the story that your house is sealed. A mouse can get through a crack the size of a quarter on it's flat side, and that's an adult mouse. But even if it is sealed, you can have tons of them living in the house.
They live in walls, floors, attics, ceilings, cellars, behind the fridge, behind and under cabinets...
If mice can find enough to eat that they can carry away, they might not leave droppings. It's only when they get so desperate that they have to lick tiny remnants of spills or crumbs that they stay around and leave evidence. That's my experience anyway.

Oh, and they are actually very smart about traps. What kind are you using and what bait are you using? Keep in mind that they produce offspring at an alarming rate.

Thanks for your input. The wild life person is using snap traps with peanut butter. He also used a very large humane trap for larger pest with fruit and peanut butter. Nothing was caught in any of the traps. He did see the evidence of a flying sqirrel in the attic. He also made the one way out for the squirrel. The very loud noise in the ceiling has stopped. But I am still hearing noise that sounds louder than what I think mice should sound. Maybe wishful thinking on my part because I am very fearful at this point. All movement except in the kitchen seem to be centered around the duct work and also the plumbing work in the major bathroom. I am at my end. I have had so many exterminators and now working with a wild life remover and none of them can seem to resolve the problem. I wonder if I can place some type of canister in the house or poison in the walls that will kill them. I don't know any more what to try. It is very expensive to continue to rid my home of this problem.

I'd rather live with the noise than the odor caused by dead mice in the walls. Mice want food and if your traps are getting tripped its beacsue they have a good food source elsewher in your home. Set traps where you foind the acorns after you remove the acorns. Do you have pet food stored in the home?

The traps are not being tripped. The acorns were found outside of the house by the front steps where there was an opening. I do not have any pets and have been watching very carefully to see if there are any bites on anything. I have found none. I even left boxes of crackers on my counter to see if there might be a nibble. Nothing.

Is this a single family dwelling?

Yes it is a single family dwelling. It is a two story house. I am also afraid that my duct work has been compromised.

I doubt if the ductwork is compromised, mice can get into holes as small as a dime. You definitely have critters but it may not be mice, bats like to get inside too and are much more difficult to catch.

I have seen mice do a lot of compromising, LOL.
Certainly not solid ducts, but they might chew through flexible ones. They will chew through whatever they can, drag food in, let it rot and get moldy, leave urine and feces, build nests out of insulation and anything else they can find, and then die and leave a stench that I find unbearable. If you see brown spots on your ceilings the size of a silver dollar, that's a dead one.
I left paper cups of bleach everywhere, and poured or sprayed bleach wherever I could too. You can't bleach too much.
I thought I had all food away and then realized the mice were taking cat and dog kibble out of the bowls, so now I have to keep the bowls right in front of me and put them in the fridge after the pets are done.

As another answer said, a mouse can go through a hole, as long as it can get it's head it. Just like a weasle, who can get through a hole smaller than it's body! Good luck with catching whatever it is.

PS; Those "plug-in" mouse sound gadgets do work! I have three of them plugged into my wall outlets in three different rooms, and not a mouse anywhere. There are none upstairs, and the cat finds a small mouse every now and then in one of those rooms.
I think Home Depot, and Target, among others sell them. They emit a very high pitched sound that drives away small varmits, and does not bother cats or dogs ears.