Something that seems to be everywhere, like the smell of your dog after his encounter with a skunk, has the quality of omnipresence.
If you keep hearing about a particular celebrity, seeing his picture on every magazine and his image on TV, you could say that he has an omnipresence. Something that appears to be everywhere at the same time also has omnipresence, like the sound of your brother's stereo, audible in every single room of your house. The Latin word for omnipresence, omnipraesens, comes from omni, "all or every," and praesens, "present."