Shielding magnetic field without mu-metal I need to shield my device from magnetic interference, including earth magnetic field (if you move device around, it might be enough to cause slight currents i guess) and magnetic field caused by power nets, wires with large currents e.t.c .
I know this could be achieved by making case out of mu-metal, but it seems that I can't find it anywhere (especially in small quantities).
So, are the other, easier ways to shield magnetic field? 
Will multiple sheets of steel work for example? 
 A: Multiple sheets of steel work nicely to attenuate magnetic fields with higher frequencies but they are not great if you want to shield against small and constant fields. 
To shield the earth's magnetic field the best material has a high permeability with almost zero hysteresis. There are some metallic glasses, such as Ultraperm, Vitrovac or Metglas that I have tested. 
Mu-metal is still somewhat exotic, as it needs to be shaped into it's final form and then heat treated and protected against shocks afterwards. It can be magnetized easily and then needs to be demagnetized again (if you need very low DC fields).
A: " Will multiple sheets of steel work for example?"
Eventually - yes
edit: Depending on the strength of the field, the frequency and how much you have to reduce it by you can try a few different approaches. Check out the faqs from any of the companies making/selling mu-metal
A: The best way to shield DC fields would be by setting up a 3-axis Helmholtz coil setup. Shielding AC fields depends on the strength of the fields. For small currents, a simple metal mesh would work (it consists of thin strands woven together like a cloak). For high AC shielding, the only way would be to go the active route, i.e. a feedback loop that adjusts the currents in a secondary RF helmholtz coil set.
