Clamping devices for hanging or pulling wellbore rod strings each feature housing with an axial bore in which a number of clamping pieces are placed to wedge in place between the housing and rod string to perform a self-tightening action against the rod string under the weight thereof due to cooperation of beveled surfaces at the bore wall and exterior of the clamping pieces. Threaded fasteners fed through the housing wall aid in placement of the slips against the rod string. For use in pulling operations, the housing is sized for receipt in the latching mechanism of a tubing elevator for support by the same, whereby the tubing elevator can be used to pull out a stuck rod string. Some embodiments feature a circumferential gap in the housing to enable the housing to be slipped laterally onto the rod string.