Hi there.
To tell you the truth your probably going to have to model that again if you want it too smooth nicely. The problem you have is when your spliting your polygons your not looping them right round. When you split the poly, continue on until you have made a complete loop. If you dont when you smooth, it will finish off all the unlooped edges into tris. you shouldnt have anyfaces with more than 4 or 3 sides. Also be carefull, i notice you have edges that lay overtop of each other.. this will also cause yuckyness. if thats a word 
hope that helps.. try modeling it with subd, and then convert it to poly after, then smooth..
There's nothing normal about normals. In FACT i think the are abnormal.