Dear Pati, It is very much possible to prepare Fe3O4 through FeSO4 + NaOH. The amount of hydroxide impurity depend upon the oxidation time of the ppt (green rust). For a while you can follow up this paper. http://www.sciencedirect.com/science/article/pii/0010938X9190016I.
From FeCl3 it will lead to FeOOH. But I am not sure which hydroxide will form if it comes out to be gamma- FeOOH you can very well reduce to Fe3O4 by annealing in vacuum.