So to clean up that part with the overlapping pieces, you'll need to use some object repair techniques, there is a tutorial on this type of stuff here:
http://moi3d.com/forum/index.php?webtag=MOI&msg=446.17
For this particular case you'd do something like this - select it and run Edit > Separate to break it into individual surfaces.
Then select these 2 surfaces (looking at the underside here), and run Edit > Trim:
At the trim prompt to select cutting objects, push "Done" or right-click in a viewport to signal you want to do a "mutual trim" where each object is both cut and used as a cutter.
Now Trim will dice up the surfaces and you'll be able to pick which pieces to remove. But in this case it's easier to pick the pieces to keep instead, so switch it to "Keep" mode and select the 2 visible pieces, there will now be an edge where they were intersected with each other:
Now there's also some overlapping pieces on the top and bottom to fix up as well. Since those are all planar, instead of trimming them with each other instead just delete all the top faces and draw in a new connector line here:
Then select the entire outline and run Construct > Planar to build just one single big trimmed plane surface for the entire bottom, it's better to have things like this as one big plane rather than a bunch of little coplanar fragments:
Then repeat that on the other side and also build a planar cap for the middle side area, then join up all those pieces and you'll have a finished well formed solid for this particular piece after that.
One shortcut is if you build the cap for the middle side area first and then join all that together so that there are planar openings on the top and bottom with the side walls all complete, you can then select the entire joined piece and use Construct > Planar to build planar end caps on it. The Construct > Planar command works either on a set of planar curves, or also if you select a joined surface object it will see if the open edges form a closed planar outline and build a plane and join it in there, that can save some steps.
Hope this helps!
- Michael