I use MIDI in OnSong and I don't think you use "MIDI files" for this. What OnSong allows you to do is to embed MIDI commands at the beginning of a lyrics/chord chart and once your system is configured OnSong sends the embedded MIDI commands when you select the chord chart.
The way I use it is to get OnSong to send MIDI program change commands to my keyboards when I change songs. That way every time I select a song in OnSong the keyboards all change to the correct sound. Very handy. All I need for that is an interface for my iPad to connect into the keyboards. I use an iConnectMIDI interface for that.

In principle OnSong should also be able to send MIDI commands to other apps on the iPad that understand MIDI - for example a suitable software synth, so you in principle you should be able to change the sound in a software synth on your iPad when you change songs in OnSong. I haven't tried this at all.

OnSong can also be configured to perform some actions in response to MIDI commands - so you could for example scroll down a chord chart by pressing a key on your keyboard. I haven't tried that and I'm not sure how to do it but I suspect you would still need some sort of interface to get the MIDI message from the keyboard to the iPad. If that's what you're interested in doing you may want to ask the OnSong support team.