The same features that generate biodiversity patterns across and within oceanic islands over evolutionary time - interactions between isolation, area, and heterogeneity - also influence their vulnerability to biological invasions. Here, we identify the factors that shape the richness and abundance of woody aliens in forest communities across the Hawaiian archipelago, and assess the relative importance of abiotic, biotic, and anthropogenic factors and their interactions on the establishment and dominance of woody alien species. Using a database of 460 forest plots distributed across the six major Hawaiian islands, we examine variation in i) relative alien species richness and abundance as a function of multiple factors (e.g., temperature, aridity, soil age, and the human influence index) and ii) establishment and dominance of alien species as a function of abiotic and anthropogenic factors, as well as phylogenetic and trait distinctiveness. We found that relative alien species richness and abundance were higher in areas where temperature was high and aridity low. Gradients in temperature, aridity, soil age, and human influence also modulated the importance of biotic factors in determining establishment of alien species. In contrast, whether these alien species could become locally dominant was not strongly influenced by abiotic or biotic factors, or their interactions. Our results suggest that environmental filtering mediates the strength of biotic filtering in determining where woody aliens are able to colonize and establish on these oceanic islands, but not whether they become dominant. The strong context dependence of multi-species invasions highlights the complexity of developing management strategies to mitigate the biodiversity and ecosystem impacts of biological invasions.