To my knowledge, there is no way to sort your inventory aside from doing it yourself. It can be a pain if you let it build up, so it's probably best to sort it as you fill it up. I use one tab for crafting ingredients, one for consumables, one for sellables, etc.
You gain access to item storage after you complete the level 15 story quests, the three "tutorial dungeons." When you finish, you can hire a retainer, which allows you to sell and store items. As far as the armoire, I can't speak to that, as I haven't tried using it yet.