I agree with Ajmooch, I think going about modeling something like that using NURBs will be more complicated than if you used an extruded poly cube.

You can go ahead and use the stitch edge tool (Edit NURBS>Stitch>Stitch Edge tool), or you can convert them to polys and combine them (Mesh>Combine) now you'll most likely have to go in and start merging verts/edges, however you want to approach it.

And as far as the extra geometry, it happens even when I have "control points" checked in the NURBs to polys convert options :/ so I guess you have to select those edges either one by one or use the edge ring, edge loop selection tools, or pick walk and delete them /shrug maybe someone can come up with something better, I don't really use NURBS a lot.