Summary: Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the general Eulerian polynomials, as defined by Xiong, Tsao and Hall [T. Xiong et al., J. Math. 2013, Article ID 629132, 9 p. (2013; Zbl 1268.11035)], are moment sequences for simple families of orthogonal polynomials, which we characterize in terms of their three-term recurrence. We obtain the generating functions of this polynomial sequence in terms of continued fractions, and we also calculate the Hankel transforms of the polynomial sequence. We indicate that the polynomial sequence can be characterized by the further notion of generalized Eulerian distribution first introduced by M. Morisita [Measuring of habitat value by environmental density method. In: G. P. Patil et al. (eds.), Statistical Ecology, The Pennsylvania State University Press, 379–401 (1971)]. We finish with examples of related Pascal-like triangles.