You can't change the image as the chat links grab the first image it sees on the page. 

For example if you insert the link of this post you created http://www.oxwall.org/forum/topic/32410 you'll see you avatar. 

Make a suggestion on uservoice: http://oxwall.uservoice.com/forums/13756-ideas-for-oxwallIn the meantime this is considered as a custom code modification. You're free to do that on your own or hire a programmer. You can do that here: http://www.oxwall.org/market/specialists
Also you can make a post in the custom code modification section of the forum, probably some community member will assist you with that. 

So i could find that image and delete it right?

Well, yes, you can do that on your website, if you don't need the image. but if a user shares 3rd party website, you can't do that for obvious reasons. 

Where can is see what image is the first on a given page of my site?  I do not even see this image?

Well, you can insert the link in the newsfeed status to see. 

that image is the power by oxwall image at the bottom of the page 

Guys, have you tried to add your custom image ?

Try to upload the image via Admin Area>Appearance>Edit Theme> Graphics section.
Then go to  Admin Area>Settings> Main Settings> Global page settings section.
Add tag <img...> to Custom head code field.
For example:
<img style="display:none;" src="here the image link" />
After this the system will grab your custom image instead of  the default one.

It would be neat of the text of the link got made from the name of the item. So if we send an event via IM, it would display the name of the event.

Yes, it works in a way you want.
For example, if you insert a link of your blog post into IM you will see that system grabs title, description and instead blog post image it will take the default image.

In case when our system should grabs unique image per each post it's requires the implementation of new system like the Open Graph system instead our using simple oEmbed system.

I am adding a comment here so i can find this at a later date if i need this.  I have had this issue for awhile and thanks to Darryl who found this post, this does seem to work.