That sounds like an actual virus in your router, I've seen that a few times.
You need to reset your router to factory defaults (there should be a reset switch somewhere on it, probably have to use a push pin to get to it, they are recessed) and setup your network from scratch. New name. New network password.
Then clear out all cookies, temporary internet files and anything like that on the computer. I would also recommend clearing out all history, saved passwords and auto-fill text. If you are using a PC, run anti-virus.