I have my two cases stored vertically between a magazine file box that holds paper and my little desk organizer that has scissors and normal pens/pencils/etc. Each one is only an inch or so wide (maybe 2?) so it doesn't take up much space at all.
Mine aren't full so I plan on sticking a small baggie of stumps in the case when I travel. Otherwise, they'll go in the zipper binder I have for other stuff, including ready to color pages! As for OMS, I'm pregnant so I can't use it. I use baby oil, and will bring my little baby food jar with a cotton make up remover circle in it (dry) as well as a travel size bottle of baby oil that will go in my toiletry bag. Or at least, that's the plan!