If you want to transfer files between windows phones, iOS devices, and Windows computers, you should give OneNote a try.
The benefit of using OneNote (instead of using OneDrive directly) is to have the files accessible offline. For me specifically, OneNote is one of the few options I have in a country that blocks anything Google, Dropbox, and BitTorrentSync. I tried Pushbullet for a while because it is cross platform, have the ability to transfer files, and works in China, but I settled for OneNote eventually because it feels more convenient. I am a heavy OneNote user to begin with.
To set this up, you will need a Microsoft account to setup an online OneNote notebook. You can do this directly using the OneNote program on your desktop, OneNote apps on any of your mobile devices, or the webapp accessible from www.onenote.com or www.outlook.com.
You "transfer" files using OneNote by pasting/sharing the file into an OneNote notebook. On the other devices, you would have to sync the notebook first or have internet access to retrieve the file. But once you sync your notebook, you can access the file offline. While the desktop versions of OneNote does automatically syncs, it doesn't seem to work on my windows phone or iOS device.
I cannot say for certain that this will work for OneNote on Android, because I do not have any android devices. I would think the chances are high though. Using the OneNote webcpp, you can also download files from any web browser that would work with it (e.g., using Chrome on Linux). However, uploading of files is not supported by the webapp.
One other alternative to share/transfer files to multiple devices is email. I.e., you can send files to yourself. For me, opening up the email client, attach files, and mail them off involves more steps than dragging a file to my OneNote notebook on the desktop. Also, I do not have email accounts setup for most of my mobile devices. The advantage of email over OneNote is that email sort of "autosync" since email apps tends to have the option to automatically download emails.