Arion pm'd me and I had some suggestions. He said he was going to ask you about some details, but I suspect he's in a different time zone... Anyway I'll repeat them here:
If you are running Kuertee's Clean Up then it's possible that this is removing some items. It goes through and removes items that you're dropped into the game world. Normally this isn't a problem with player houses because he would mark those as "safe" zones. I suspect that mod houses are not marked that way. I had this happen to me with Battlehorn Castle (the DLC). I had dropped some Black Horse Courier's on a table and when I entered the cell again, they were gone. Apparently you can add "safe" zones to Kuertee's Clean up so that it doesn't remove items in that cell. I'd check the readme or documentation to see how to do that. I don't run KCU anymore, so I can't help with that.
For vanilla items falling through furniture, that's a well known problem. Basically it would require the collision to be redone on all vanilla items and nobody has jumped to volunteer for that job Personally I run Decorator Assistant and use its lock in place - permanent function to stop that from happening.
I'm not sure about the chest and items getting a stolen flag on them. I know that Enhanced Economy has a new setting that will make looting the public barrels and crates in cities illegal. Same for crops in farmers' fields. Now the way that TheNiceOne does that is automatic when you open the container. It's possible that the ownership for the cell that you are dropping the chest in has not been assigned to the player, so EE thinks that it's owned by somebody else, so items are being flagged as stolen when you retrieve them. There is a button you can hold down while opening the container that stops this behaviour, I believe, so you could look up what that is and try doing it and see if that corrects the problem. If you're running EE that is If that is the case, you could contact the mod author of the house mod and ask them to change the ownership, but I don't know what implication that would have with companions. I wouldn't think that EE would flag the item as stolen if there was no cell ownership at all, though. So that seems to indicate that is has been set to something specific that isn't the player.
If you're not running EE, then the cell that you're dropping the chest in must be owned by someone other than yourself. Basically the ownership is not set on anything purchased from Imperial Furniture. This is usually not an issue and actually helps IF furniture be compatible with companions (it allows them to use the beds and stuff). However this does mean that if you drop something in a cell owned by someone else, that item will inherit the ownership of the cell you drop it in and you will be stealing if you pick it up. That's the way Oblivion works actually and it's intentional. It means that all you have to do is set the ownership on a cell and you don't have to worry about going around and setting the ownership for every single item in the cell. I've gotten caught by this a couple of times myself. I find it easier when testing to drop stuff right in the store, but when I want to pick it up again, I'll have Damien yelling at me There seems to be a timing issue involved though. I don't know if the game needs to go through the normal cell reset sequence for that to take effect or not - it might.
Lastly if you are having problems with Imperial Furniture items falling through the floor of house mods, then the collision of the floor on the house mod in question needs to be fixed. I tried to test the new pedestals rather thoroughly to make sure they didn't fall through the ground and I think I got the collision fixed so that that wouldn't happen. I actually enjoyed throwing the pedestals at the guards near Imperial Furniture and at the guards in Battlehorn Castle Those were my two main testing areas although I did test in the Chorrol player house too. So basically I tested the ground outside and floors in various locations.
So I think you've got a bunch of things going on that may or may not be related to the house mods you're running, but hopefully this will give you some ideas.
Edit: If is was Kuertee's Clean up that removed the items, apparently there is an area that they get stored in for a while so that you can get them back. I don't know how long they are kept there though. Once again have a look at the documentation and you could try to get them back.