I'm having lot of trouble modeling a room, the general problem is that lines overlap. I tried removing doubles but nothing (all the mesh was selected). There must be something i'm not doing right but i don't know what
Looks like you don't have duplicate vertexes. Looks like you have an edge on the inner vertexes and another edge from the farthest vertexes. The edges overlap where you circled. You can try to delete the edges and create them correctly, then recreate the needed faces.
If it's just one or two vertexes, merge them by selecting both, then clicking alt-M.
If it's multiple vertexes, run Mesh > Remove Doubles over it. If this still doesn't do the trick, take a look at the lower-left panel in the 3D window: the Remove Doubles Merge Distance can be increased to be more tolerant.
It's likely you got lots of doubles from applying an extrude operation, and then Undo-ing it. Extruding is two operations in one: it duplicates the vertexes selected, and then puts you in a transform mode. Undo-ing once only stops the extrusion: the vertexes have still be created. You'll need to Undo twice to remove the overlapping vertexes.