I am again changing the systems in place around the amount of items you can keep in your inventory.
A normal Pokemon can carry up to three items without a bag(Though be warned it would hinder them as they'd have to carry it all in their arms/jaws)
Of course if you have your own bag you can carry slightly more, but you'll need to clear that and the amount of items it can carry when you create your character.
As for the treasure bags that are handed out when you register at the Guild. When you are first given one, it can hold up to 15 items. However, as you rise through the ranks, you will be given larger treasure bags. Note that your explorer badge and wonder map do not count as items.
If you have too many items whilst in a dungeon, you will need to drop some. You cannot carry more.
Once out of the dungeon however, you can then store those items in your guild room or house/home area. Please make sure that you finish your threads before doing this though. I will be checking ^^