Invasions of microbial communities by species such as pathogens can have significant impacts on ecosystem services and human health^1–9. Predicting the outcomes of these invasions, however, remains a challenge. Various theories propose that these outcomes depend on either characteristics of the invading species^10–12 or attributes of the resident community^13–16, including its composition and biodiversity^3,17–19. Here we used 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 found that the communities with fluctuations in species abundance are both more invasible and more 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. Although diversity-invasibility relationships are qualitatively different depending upon how the diversity is changed, we provide a unified perspective on the diversity-invasibility debate by showing a universal 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, in this regime of strong interspecies interactions, if an invasion is successful, it causes larger ecological effects on the resident community than when interactions are weak. Our results demonstrate that the invasibility and invasion effect are emergent properties of interacting species, which can be predicted by simple community-level features.