Can I carry things inside of monsters?

Yes it's possible. Rather than trying to use the physics object grab or spamming Fus Ro Dah however, a better choice is to use one of the 'raise dead' spells from the Conjuration school. This will allow your Skeever Suitcase (or Bandit Backpack, Draugr Drawer, Vampire Valise, Necromancer Knapsack, Stormcloak Satchel, or even Legionairre Luggage - whatever is handy really) to follow you through cave, town, building, and zone entrances, offering much more versatility.

Theoretically, yes it is possible. How you do this varies from fireballs to FUS'RO'DAHing him all the way home.

Only way I see this not working is if it is inside a dungeon (read: an area that requires a loading screen to get in/out of) the body would probably be permanently stuck inside the area.