Finder problems

I am running OS X 10.9.4 and have suddenly come up with a problem. after I open a .dmg file and the disk image appears in the Finder, I am unable to drag the icon to the trash or right-click "Move to Trash".. The only way to remove the disk image icon is to either log out and in or to use the Disk Utility program

What do you mean "unable?" You mean the icon won't move? Or it moves but snaps back? Or you get an error message saying something? What happens when you try moving/right-clicking?

Thanks for your reply.

When I right click on the icon of the disk image on the desktop, a contextual menu appears, but it does not include a menu item for "Move to Trash" or "Eject".

When I click-hold on the icon and move it around the desktop, the original icon stays in place (i.e., I am moving a copy of the icon) until I lift my finger, when the original jumps to the location of the copy and disappears from its initial place. When I do the same thing and place the icon in the trash, the original icon stays in its initial location and nothing goes into the trash.

Finally, Command-E does not work on a selected disk image.