To do this in the built-in Mail app, locate the attachments at the bottom of the email message and tap to view full screen. If you have received a single-page PDF file, the Mail app will treat this as an inline image for you to view readily. You can tap or double-tap on this image to view in a full-screen preview.
Once previewing the image, locate the share icon that looks like a square with an up-arrow. This will open the Share Activity Menu. Ensure that the Add To OnSong action is enabled and then tap on it in the list of actions. This will enqueue the file for import the next time OnSong is opened.
You can then repeat this step for every file attachment that you want to import.