In this paper, we characterize the detection thresholds in six orthogonal modes of vibrotactile haptic display via stylus, including three orthogonal force directions and three orthogonal torque directions at the haptic interaction point. A psychophysical study is performed to determine detection thresholds over the frequency range 20-250 Hz, for six distinct styluses. Analysis of variance is used to test the hypothesis that force signals, as well as torque signals, applied in different directions have different detection thresholds. We find that people are less sensitive to force signals parallel to the stylus than to those orthogonal to the stylus at low frequencies, and far more sensitive to torque signals about the stylus than to those orthogonal to the stylus. Optimization techniques are used to determine four independent two-parameter models to describe the frequency-dependent thresholds for each of the orthogonal force and torque modes for a stylus that is approximately radially symmetric; six independent models are required if the stylus is not well approximated as radially symmetric. Finally, we provide a means to estimate the model parameters given stylus parameters, for a range of styluses, and to estimate the coupling between orthogonal modes.