The outcomes of ecological invasions may depend on either characteristics of the invading species or attributes of the resident community. Here we use a combination of experiments and theory to show that the interplay between dynamics, interaction strength and diversity determine the invasion outcome in microbial communities. We find that the communities with fluctuating species abundances are more invasible and diverse than stable communities, leading to a positive diversity-invasibility relationship among communities assembled in the same environment. As predicted by theory, increasing interspecies interaction strength and species pool size leads to a decrease of invasion probability in our experiment. Our results show a positive correspondence between invasibility and survival fraction of resident species across all conditions. Communities composed of strongly interacting species can exhibit an emergent priority effect in which invader species are less likely to colonize than species in the original pool. However, if an invasion is successful, its ecological effects on the resident community are greater when interspecies interactions are strong. Our findings provide a unified perspective on the diversity-invasibility debate by showing that invasibility and invasion effect are emergent properties of interacting species, which can be predicted by simple community-level features.