This is mostly a note to myself, but I thought I'd share it in case it helps somebody.
To get an Eagle PCB board outline & drills into Inventor, you use the DXF export utility in Eagle.
Before exporting, make sure Eagle is only displaying the following layers, assuming you're using the default layer setup:
17 - Pads
20 - Dimension
44 - Drills
45 - Holes
46 - Milling
(Note, you might want to select additional layers, but I'd start with these first, because Inventor chokes on more.)
Next, click File/Export/DXF and save your file someplace. I stick them in a sub-folder of my Eagle project named "Export".
Now go to Inventor and open the DXF file. An import routine will be triggered, use these values:
Selective Import, layers 20 and 44. Look at the drawing to confirm you're getting what you want.
Check - Wires
Specify units - mm (if that's what you used in Eagle)
Check - Constrain End Points and Apply Geometric Constraints
Select "New Part - Project wires to 2D sketch"
Mapping options - Check "Map all layers ... single sketch"
Tada! There is your board as an Eagle sketch, properly sized, ready for extrusion.
Now, you might ask, "Why are you displaying those layers in Eagle for the export, but then ignoring them in Inventor?" The answer - it looks like Eagle has a bug. Without enabling all those layers, the drills don't come across. At all. Frustrating, but surmountable.
Also... if you're getting your boards made by OSHPark.com, then you can go ahead and extrude the board at 1.8mm in thickness. This is the same value for both 2 and 4 layer boards.