"We have visitors."
Translation:Vi har besøk.
"Besøk" is just a general term for when you have somebody over at your house. So it could very well be both one and several persons you're referring to when you state that "jeg har besøk". You can refer to the people who are "på besøk" (on a visit), as "besøkende" (visitors). For example "Jeg har aldri før hatt så mange besøkende på én gang" (I have never before had this many visitors at once).
I hope that can be helpful :)
That would be a nice etymology but the internet seems to disagree. Apparently it's from ber-serkr = bear-shirt http://etymonline.com/index.php?allowed_in_frame=0&search=Berserk