If the pics are hosted on your own site Thurston it is OK to use them but if you are not hosting yourself this is called hot linking and is quasi-illegal and can be considered theft of bandwidth.for example I used one of your images last week on another thread on here "I am lazy"
https://community.auctiva.com/eve/forums/a/tpc/f/455609321/m/3081050762/p/1 and I hosted it on Auctiva. So in short if the pics on emotipics are yours I see no reason you cannot post them here. I have never actually heard of an individual getting in trouble for it. But...
Edit: More than likely you already knew this but I am going to leave the post for others to see that may not be aware of this.
Edit/Edit
I am testing straight from your site to see if your links work with this pic. Hope you do not mind?
Did not work for me I uploaded the image to Auctiva and it should now, kind of strange if you ask me!