Today I had a much clearer answer to this question (from the Open Graph debugger tool):

Small og:image: All the images referenced by og:image should be at least 200px in both dimensions, with 1500x1500 preferred. (Maximum image size is 5MB.) Please check all the images with tag og:image in the given url and ensure that it meets the recommended specification.

og:image should be larger: Provided og:image is not big enough. Please use an image that's at least 200x200 and preferably 1500x1500. (Maximum image size is 5MB.) Image ... will be used instead.

So, YES, you have to convert your open graph images to at least 200x200 pixels, and it seems that the larger, the better.

If your image is smaller than 200x200, Facebook will try to use a larger image (if) available on the page.

The same information returned by the debugger can be found on the open graph documentation, on "Maximizing Distribution for Media Content" topic, item 3: tags

My experience with Facebook made me doubt that computers are deterministic machines :)

Sometimes it will accept image of any size (between 200 and 1500px), sometimes complain that image is too small (og:image should be larger) even if image is squared and bigger than minimum size (e.g. 400x400px). I had situations where the same link showed all 3 og:images in linter and in FB status field, then suddenly 2 weeks later stopped working and started showing only one image while trying to share it in FB status field (linter still showed all 3 images), and vice versa. Sometimes FB seems to have problems with different domains (e.g. page is on www.example.com and og:image on www.picdumpexamplesite.com), sometimes it doesn't mind...

IMHO it's heavily broken, and the best you can do is:
- make images squared, rounded to "hundreds", e.g. size 300x300px
- host them on the same server (same domain name)
- use jpg
- avoid any "strange" chars in filename (I use only letters and numbers)
- pray that something of the above works :)