In Synchronous select the part or assembly (assy would be the same in ordered) and rotate it using the steering wheel after selecting the correct axis. It may require two rotations to get it the way you want it. You also might want to move it to get it situated on the coordinate axes.
In ordered you should be able to use Home/modify/rotate faces then select body.
The way I do it and this may not be the best or quickest way, is via insert part copy
Open the downloaded file in SE and save as PAR.
Open a new PAR (in ordered) and use the abilities with either a mirror or a different coordinate system.
Once the 3D model is in the correct orientation, move all to synchronous (breaking the link to the original) and voila, you have the e3D model in the orientation you want it to be....
Another way to skin the cat is to pull the downloaded part into a new blank assembly and assemble it into the desired orientation. Then save the assembly out as a parasolid and pull it back into SE again as a part and save. You will then have the part in the desired orientation. Clean and simple with a minimal feature tree just like the original downloaded part.
As an aside -- if the downloaded part is actually an assembly and you are going to convert it to a single part -- and you wish to alter the colors of the parts, do it before saving out to the parasolid mentioned above. It is often easier to change the colors at this stage rather than tediously selecting faces in the single part later on.