Our Hoover HNV380 Nextra8 also had the problem of a screeching noise when rotating in one direction.
I followed Osteopaths instructions to remove the front panel (thanks Osteopath). Having found the motor and the two plastic tension pulleys, I removed the whole pulley tension mechanism by opening the spring loaded jaws of the pulleys and slipping off the drive belt. Then by opening the other end of the jaws the whole mechanism can be removed from the spindle (need strong fingers). Having the pulley in my hand I could tell just by turning the pulleys that they were the problem. I cleaned them with copious WD40 and then lubricated them with high melting point grease, applied with the back of a knife down the sides of the pulleys and onto the pulley shafts. Put the tension pulley system back is the reverse of removal. Put the belt back on, I used some masking tap to hold the belt on the drum while putting the belt back on the motor spindle and tension pulleys. Make sure in runs in the middle of the pulleys by moving it up and down the motor spindle and turning the drum. I don't think our belt was centrally located to start with which may have added to the problem as this would have forced the pulleys onto one side of the carrier mechanism and cause extra wear.
Machine is now running as good as new. Happy mending.
Tim, October 2013