I'm pretty new to 3D design and to MOI in particular but have progressed far enough to attempt a Moebius strip. After several false starts and forum searches I managed to produce one by creating it a half at a time using sweep with two rails.
Inspired by Andrei Samardac's enthusiasm for the LOFT function, and knowing that my strip did not have to have precise geometry or dimensions I gave it a go using LOFT and I'm happy with the result. I'll post below a photo of the resultant 3D print.
Here's the method that I used:

1. 2 short lines in the negative x direction, spaced apart, starting from the y axis.
2. A Freeform curve connecting these two lines and approximating half of the desired path of the strip centre line.
3. Join these three line.
4. Mirror about the y axis. Do NOT Join.
5. Draw required strip cross section (profile) using 'Rectangle with rounded corners' appropriately positioned at the start of the first curve.
6. Use Array-curve to position 6 copies along the first curve.
7. Use CPlane to facilitate rotating each profile copy by 15 degrees more than its predecessor.
8. Select all 7 profile and hit LOFT - I used Loose and Exact Loft options, though Normal and Exact work fine also.
9. Repeat steps 6,7 and 8 on the second (mirrored) curve.
10. Boolean-join the two solids.

This method may well be a bit clunky, no doubt my Sweep based method was, too. Comparing the two methods that I used for this 'freeform' shape I preferred Loft for 2 reasons:
1. It was quicker. The methods were very similar but for the Sweep method I had to draw the rails, which are not required for Loft.
2. A cleaner result. Using Sweep I was unable to get the far end of the swept solid square with the x,y,z axes and had to separate the two swept solids and join them using the magic of Blend. No such problem with the Loft method.

I'd appreciate any tips on how to improve the method described.