Yeah it is hard to believe Maarten, that's what my brother said.
What I do is I take my character and give him the easiest major attributes (ie athletics, acrobatics, blade / blunt, block, light / heavy armor) and start using them. You may think athletics is a bit difficult, but it is not really that complex. A little trick I learned from Morrowind is to go to the nearest river (preferably one with a wall) and equip a ring that gives you water breathing. Keep swimming into the wall (underwater) and you will get your athletics jacked up. I assure you, it's not cheating! Lol
To make things easier, you could put a weight on the control. For PC, I stick a metal die on the "W" key. Since you have a 360? You could put a rubber band and wrap it around the movement toggle and see what happens

Anyway, the other skills beside acrobatics can be used simultaneously. Enter the arena, and breeze through it once you get the harder enemies. I think it is one or two ranks behind grand champion where you fight the three bandits. A three on one battle. Have them beat up on you to get your light / heavy armor skill get pumped up. If you want, bring a shield and block their attacks to raise your block as well. Or, if you do not like being beat up, kill them all with a weapon to raise your blade or blunt. Either way, you will get alot of levels no doubt.
Once you complete the whole arena faction, you will be able to fight creatures weekly, this is free gold and levels. Take your equipment and fight, pick the option that you want to kill three monsters and off you go.
Like explained, either - block their shots, get beat up, or kill them all.
You can keep doing this weekly, it really is not that hard.
In the beginning, if you pick armorer as a major skill, you are in luck.
Every time you get beat up, repair your armor; or, if you think there is a better way, there is.
In the Shivering Isles, do the quest "The Coming Storm", there is an artifact called "The Amulet of Disintegration" TAKE THAT. Keep equiping and unequiping it. Your armor will be breaking and breaking, that gives you the whole advantage of repairing it. Sweet eh? I got my armor maxed from one using that secret - well, it is not really a secret but still.
If you pick alchemy as a major skill, I always tried to make really good poisons. Poisons are: A) good for killing things with, B) easy to make and good for alchemy, and C) making good cash.
Some of the best poisons you can make are in the oblivion planes, use the spiddal sticks and blood grass. Cool thing is, you will never run out of them because there are so many of them! I kept finding it dreadful to run back and forth in the wilderness harvesting ingredients and never found enough. But oblivion planes are all over the place, it could not be easier.
Well, as for acrobatics, there are a bundle of ways to train it, but the best ways are just jumping off cliffs. The camp Dive Rock is probably the biggest cliff you can jump off. It sounds wrong, but I raised my level off that cliff one too many times. There are also multifarious spots on the Shivering Isles that you can jump off, there is a large waterfall near Crucible that you can jump off. BUT BE WARNED! The waterfall is very dangerous and guaranteed instant death, I would go there if you were 90 acrobatics, OR, you could wear the boots of springheel jack and see what happens.
Ah, well that is all I can tell you on how I got my combat level so high, mostly it was stuff I knew from Morrowind, but meh.
Oh and to answer your question, no there is not any storage facilities on Shivering Isles. It truly is a bummer, but there is not much you can do. Oh, and here is a little advice, do NOT put any items of yours into containers anywhere in the Fringe. They will disappear one way or another.
~Weekend Dude~