I have a similar set of .iml files, like yours, using the old version of Android Studio, but after upgrading to a later version, he created another .iml, so there was a top-level project.iml project with a module containing module.iml and module-module.iml.
As far as I could tell, the module-module.iml file was useless, and the key information was in the .iml module. However, even if I delete all the iml files, Android Studio will restore them all, so I realized that it stores enough information in [project] /. Idea / modules.xml to recreate iml files from scratch.
So, I left Android Studio, deleted the .idea folder and .iml files, and then restarted Android Studio and imported the project using build.gradle files. He recreated only project.iml and module.iml, and everyone is happy.
SUMMARY: As long as your gradle.build files are clean, you can delete the .idea and .iml files, import the project using gradle files, and get a nice clean project structure.
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