Howdy, and welcome (back)! :wave:
Have you read this yet? http://www.uesp.net/wiki/Oblivion:Oblivion_for_Morrowind_players. It's been ages since I've played MW, but I was going to ask if you'd slept yet, or just been waiting, because a difference in leveling up seemed familiar. Glad you got it sorted!
Another big difference between the two is the way the world levels with you. In Morrowind, it was better to do the MQ, Tribunal, and Bloodmoon after certain levels because if you did them sooner, you'd die horribly. In Oblivion, you can do any of the quests and factions whenever you want, and generally the enemies will always be around the same level as you. Rewards will usually be leveled to you as well, so that's the main reason why a lot of people wait until level 20 or above before doing certain quests, so they can get the best possible rewards.
Very basically, the usual route is factions >MQ >Knights of the Nine >Shivering Isles. That lets you do some training before tackling the bigger questlines. If you're roleplaying though, the order depends a lot more on who the character is, and if they'll even do certain quests (my first character was an Orc who'd started in Morrowind, and didn't like the Empire very much, so he pretty much told the Blades where to put their katanas :laugh:). You can also wait until around level 30 and do SI first, just to get some really good gear before doing the MQ -- however, you can also do KotN first (and much sooner), since that gear will level up with you (it's the only gear in the game that will).
Personally, I suggest that you just do whatever, whenever, and experience the basics of the game with this character. Find one of the guildhalls for the Mages Guild and join them, so you can get your recommendations and gain access to the Arcane Uni. Don't have to do the rest of the questline yet if you don't want to, the main reason you want in there is so you can make your own custom spells and enchantments. Custom spells are usually much more effective than those you can buy, and you'll have the benefit of crafting something that suits your playstyle. Later on, you might want to make new characters who only do certain parts of the game. Or go visa-versa, and only do some parts with this character, then make other characters who'll experience other parts.
Hope that answers some questions, and don't be afraid to ask more, we're a friendly bunch