get rid of random string before an for an image path on wordpress

I see what you’re talking about. Looks like the images are being generated by the timthumb script and that slug references a cached image identifier. Without seeing the plugin or script thats generating those images, its hard to say how to fix it.

On first view of an image, the image path looks like
http://tambnguyen.com/wp-content/themes/13Floor/timthumb.php?src=thumbs/Linus_Lundin.jpg&h=136&w=136&zc=1

and after refreshing, its more like
http://tambnguyen.com/wp-content/themes/13Floor/ic.ab271bb704a7768685cd1f6d6cd3eb8f.136x136xtimthumb,ophp?src=thumbs,_Linus_Lundin,j&h=136&w=136&zc=1.jpg

Either way probably doesn’t work for facebook sharing.

Why not just include the raw image (ie. not processed through timthumb) in a hidden div in your single.php template? That way you have something to show if you want to share the post on facebook?