Ii have just experienced this problem on OS X 10.9.5; Ii had set up Time Machine with a new destination volume, and it backed up normally for three days. Then Idays; then i got errors pretty much identical to yours on every backup attempt.
Ii found that Ii also couldn't create files on the backup destination volume via Finder or terminal. TheTerminal; the error message in terminal was "xyz: invalid argument" where xyz was a file Ii was trying to create via touch or echo.
Thethe permissions on the volume looked normal, so Ii decided to give the OS a fresh look at the volume by ejecting it (had to force eject), then remounting via Disk Utility. AfterUtility; after that Time Machine completed a backup successfully.