I purchased this Omega case Ref 166.0212 from a friend a few weeks ago and I haven't been able to find any info as to what movement this case takes. Case comes crown and nos dial, is a medium size case 30.32 mm excluding crown. The back of dial is stamped 440 685 , 1711 ZJ

 

http://boley.de/en/case-parts/omega/4194

There is a reference number 684 in this listing. That might just be the movement you are looking for!

http://www.ranfft.de/cgi-bin/bidfun-db.cgi?10&ranfft&&2uswk&Omega_684

The small size fits well with the large movement holder ring seen in your first picture.

Good luck with a nice project!!