Lenny is rabidly awaiting Oblivion for PS3

You have a weight limit (at least if you plan on moving), based on your strength. You can carry everything your heart desires, as long as it doesn't add up to your maximum encumberance or more.

Speaking of encumberance, it only prevents you from moving, and only while you're in control. So, when you're cleaning out that dungeon, take a feather spell or pots with you. As you clear it, take all the loot to the top and dump it just inside, carrying as much as you can and keeping only your gear on you. When you're done, give yourself feather for an encumberance boost, grab all you can carry, step outside, and fast travel to someplace you can sell your loot. Your feather effect will allow you to get there, no matter how far, as long as you fast travel there while it's still active. Be prepared to repeat at the other end, however, since it usually will have worn off. You still have to make several trips, but this way, you make fewer.