The orbit distribution of young stars in the Galactic disk is highly structured, from well-defined clusters to streams of stars that may be widely dispersed across the sky, but are compact in orbital action-angle space. The age distribution of such groups can constrain the timescales over which conatal groups of stars disperse into the "field." Gaia data have proven powerful in identifying such groups in action-angle space, but the resulting member samples are often too small and have too narrow a color-magnitude diagram (CMD) coverage to allow robust age determinations. Here, we develop and illustrate a new approach that can estimate robust stellar population ages for such groups of stars. This first entails projecting the predetermined action-angle distribution into the 5D space of positions, parallaxes, and proper motions, where much larger samples of likely members can be identified over a much wider range of the CMD. It then entails isochrone fitting that accounts for: (a) widely varying distances and reddenings; (b) outliers and binaries; (c) sparsely populated main-sequence turnoffs, by incorporating the age information of the low-mass main sequence; and (d) the possible presence of an intrinsic age spread in the stellar population. When we apply this approach to 92 nearby stellar groups identified in 6D orbit space, we find that they are predominantly young (<~1Gyr), mono-age populations. Many groups are established (known) localized clusters with possible tidal tails, while others tend to be widely dispersed and manifestly unbound. This new age-dating tool offers a stringent approach to understanding on which orbits stars form in the solar neighborhood and how quickly they disperse into the field.