This paper presents multiple question generation strategies for document-level event argument extraction. These strategies do not require human involvement and result in uncontextualized questions as well as contextualized questions grounded on the event and document of interest. Experimental results show that combining uncontextualized and contextualized questions is beneficial, especially when event triggers and arguments appear in different sentences. Our approach does not have corpus-specific components, in particular, the question generation strategies transfer across corpora. We also present a qualitative analysis of the most common errors made by our best model.