I wish I'd known about the following when I moved here:
There are two locations, near Diebsteich (Altona) and near Wandsbek. I went to the one near Diebsteich this week for the first time and think it is just what you're looking for.
The furniture is cheaper, but delivery is 45 euros, plus 5 euros for every floor over the 1.OG. The delivery company at IKEA charges 29 euros up to a certain percentage of the price (something like 200 euros, I think) and nothing extra to carry it upstairs. If you know exactly what you want from IKEA, you can order it online for a flat shipping rate (39 or 49 euros) and never even hit the store.
Stilbruch also has a Verbrauchermarkt online, where you can post things you're looking for and find things people are offering, either for free or for a cheap trade.
Another place to seek and find free things is Freecycle. There is a yahoo! group for Hamburg.
Also, students list things for sale at http://www.campus-hamburg.de/kleinanzeigen/
Some supermarkets and Budni have posting boards where people offer things for sale -- another good way to practice your German
Hope this helps!